LMFDB - Embedded newform 264.2.z.b.19.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [264,2,Mod(19,264)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(264, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("264.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	264.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.10805061336$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	264.19
Dual form			264.2.z.b.139.7

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.274235 - 1.38737i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-1.84959 - 0.760930i) q^{4} +(1.03968 - 1.43099i) q^{5} +(-1.40421 + 0.167908i) q^{6} +(0.430909 - 1.32620i) q^{7} +(-1.56291 + 2.35739i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-1.70020 - 1.83484i) q^{10} +(-2.97889 - 1.45816i) q^{11} +(-0.152133 + 1.99421i) q^{12} +(2.66400 - 1.93551i) q^{13} +(-1.72176 - 0.961520i) q^{14} +(-1.68223 - 0.546590i) q^{15} +(2.84197 + 2.81482i) q^{16} +(-2.21773 + 3.05245i) q^{17} +(0.593615 + 1.28360i) q^{18} +(-0.399566 + 0.129827i) q^{19} +(-3.01186 + 1.85563i) q^{20} -1.39445 q^{21} +(-2.83992 + 3.73294i) q^{22} -1.44940i q^{23} +(2.72498 + 0.757945i) q^{24} +(0.578275 + 1.77975i) q^{25} +(-1.95471 - 4.22674i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.80615 + 2.12504i) q^{28} +(2.45128 - 7.54427i) q^{29} +(-1.21965 + 2.18398i) q^{30} +(-0.816325 - 1.12358i) q^{31} +(4.68456 - 3.17094i) q^{32} +(-0.466268 + 3.28369i) q^{33} +(3.62669 + 3.91390i) q^{34} +(-1.44978 - 1.99544i) q^{35} +(1.94361 - 0.471557i) q^{36} +(8.91884 + 2.89791i) q^{37} +(0.0705429 + 0.589948i) q^{38} +(-2.66400 - 1.93551i) q^{39} +(1.74848 + 4.68744i) q^{40} +(3.29058 - 1.06918i) q^{41} +(-0.382407 + 1.93462i) q^{42} -3.60336i q^{43} +(4.40016 + 4.96373i) q^{44} +1.76880i q^{45} +(-2.01086 - 0.397477i) q^{46} +(0.727433 - 0.236357i) q^{47} +(1.79883 - 3.57270i) q^{48} +(4.08999 + 2.97155i) q^{49} +(2.62775 - 0.314213i) q^{50} +(3.58836 + 1.16593i) q^{51} +(-6.40011 + 1.55278i) q^{52} +(-2.54374 - 3.50116i) q^{53} +(1.03734 - 0.961215i) q^{54} +(-5.18369 + 2.74674i) q^{55} +(2.45290 + 3.08856i) q^{56} +(0.246945 + 0.339891i) q^{57} +(-9.79446 - 5.46973i) q^{58} +(3.69578 - 11.3745i) q^{59} +(2.69552 + 2.29103i) q^{60} +(8.45451 + 6.14256i) q^{61} +(-1.78268 + 0.824422i) q^{62} +(0.430909 + 1.32620i) q^{63} +(-3.11460 - 7.36880i) q^{64} -5.82447i q^{65} +(4.42782 + 1.54739i) q^{66} +9.95011 q^{67} +(6.42459 - 3.95824i) q^{68} +(-1.37846 + 0.447890i) q^{69} +(-3.16600 + 1.46415i) q^{70} +(-7.57332 + 10.4238i) q^{71} +(-0.121217 - 2.82583i) q^{72} +(-9.14630 - 2.97181i) q^{73} +(6.46632 - 11.5790i) q^{74} +(1.51394 - 1.09994i) q^{75} +(0.837822 + 0.0639152i) q^{76} +(-3.21744 + 3.32227i) q^{77} +(-3.41583 + 3.16518i) q^{78} +(4.69761 - 3.41302i) q^{79} +(6.98271 - 1.14034i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.580949 - 4.85846i) q^{82} +(-8.86730 + 12.2048i) q^{83} +(2.57916 + 1.06108i) q^{84} +(2.06230 + 6.34711i) q^{85} +(-4.99919 - 0.988166i) q^{86} -7.93251 q^{87} +(8.09320 - 4.74342i) q^{88} +10.9210 q^{89} +(2.45398 + 0.485067i) q^{90} +(-1.41893 - 4.36703i) q^{91} +(-1.10289 + 2.68080i) q^{92} +(-0.816325 + 1.12358i) q^{93} +(-0.128428 - 1.07404i) q^{94} +(-0.229638 + 0.706752i) q^{95} +(-4.46336 - 3.47541i) q^{96} +(-11.2144 + 8.14771i) q^{97} +(5.24426 - 4.85943i) q^{98} +(3.26706 - 0.571268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{3} + 4 q^{4} - 12 q^{9} + 4 q^{11} + 6 q^{12} - 16 q^{14} + 20 q^{16} - 5 q^{18} + 25 q^{20} + 3 q^{22} + 20 q^{24} - 4 q^{25} + 4 q^{26} + 12 q^{27} - 25 q^{28} - 10 q^{30} - 4 q^{33} + 4 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) $ 48 * q + 12 * q^3 + 4 * q^4 - 12 * q^9 + 4 * q^11 + 6 * q^12 - 16 * q^14 + 20 * q^16 - 5 * q^18 + 25 * q^20 + 3 * q^22 + 20 * q^24 - 4 * q^25 + 4 * q^26 + 12 * q^27 - 25 * q^28 - 10 * q^30 - 4 * q^33 + 4 * q^36 + 26 * q^38 - 65 * q^40 - 60 * q^41 - 4 * q^42 - 43 * q^44 - 5 * q^46 + 5 * q^48 - 12 * q^49 - 80 * q^50 - 15 * q^52 - 14 * q^56 + 73 * q^58 - 8 * q^59 - 25 * q^60 - 45 * q^62 - 38 * q^64 - 13 * q^66 + 8 * q^67 - 55 * q^68 - 40 * q^70 + 20 * q^72 + 60 * q^74 - 36 * q^75 + 46 * q^78 - 12 * q^81 - 35 * q^82 - 100 * q^83 + 45 * q^84 + 81 * q^86 - 18 * q^88 + 96 * q^89 + 10 * q^90 - 20 * q^91 + 59 * q^92 + 35 * q^94 - 40 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.274235	−	1.38737i	0.193913	−	0.981019i
$2$	0.274235	−	1.38737i	0.193913	−	0.981019i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−1.84959	−	0.760930i	−0.924795	−	0.380465i
$5$	1.03968	−	1.43099i	0.464957	−	0.639959i	−0.510570	−	0.859836i	$-0.670566\pi$
$5$	1.03968	−	1.43099i	0.464957	−	0.639959i	0.975528	+	0.219877i	$0.0705657\pi$
$6$	−1.40421	+	0.167908i	−0.573266	+	0.0685482i
$7$	0.430909	−	1.32620i	0.162868	−	0.501257i	−0.836005	−	0.548722i	$-0.815114\pi$
$7$	0.430909	−	1.32620i	0.162868	−	0.501257i	0.998873	+	0.0474657i	$0.0151145\pi$
$8$	−1.56291	+	2.35739i	−0.552573	+	0.833464i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−1.70020	−	1.83484i	−0.537650	−	0.580228i
$11$	−2.97889	−	1.45816i	−0.898168	−	0.439652i
$11$	−2.97889	−	1.45816i	−0.898168	−	0.439652i
$12$	−0.152133	+	1.99421i	−0.0439169	+	0.575678i
$13$	2.66400	−	1.93551i	0.738862	−	0.536815i	−0.153493	−	0.988150i	$-0.549052\pi$
$13$	2.66400	−	1.93551i	0.738862	−	0.536815i	0.892355	+	0.451335i	$0.149052\pi$
$14$	−1.72176	−	0.961520i	−0.460160	−	0.256977i
$15$	−1.68223	−	0.546590i	−0.434350	−	0.141129i
$16$	2.84197	+	2.81482i	0.710493	+	0.703705i
$17$	−2.21773	+	3.05245i	−0.537879	+	0.740327i	−0.988306	−	0.152487i	$-0.951272\pi$
$17$	−2.21773	+	3.05245i	−0.537879	+	0.740327i	0.450427	+	0.892813i	$0.351272\pi$
$18$	0.593615	+	1.28360i	0.139916	+	0.302547i
$19$	−0.399566	+	0.129827i	−0.0916666	+	0.0297843i	−0.354491	−	0.935059i	$-0.615346\pi$
$19$	−0.399566	+	0.129827i	−0.0916666	+	0.0297843i	0.262825	+	0.964844i	$0.415346\pi$
$20$	−3.01186	+	1.85563i	−0.673472	+	0.414931i
$21$	−1.39445			−0.304294
$22$	−2.83992	+	3.73294i	−0.605474	+	0.795865i
$23$		−	1.44940i		−	0.302222i	−0.988517	−	0.151111i	$-0.951715\pi$
$23$		−	1.44940i		−	0.302222i	0.988517	−	0.151111i	$-0.0482850\pi$
$24$	2.72498	+	0.757945i	0.556234	+	0.154715i
$25$	0.578275	+	1.77975i	0.115655	+	0.355950i
$26$	−1.95471	−	4.22674i	−0.383350	−	0.828933i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−1.80615	+	2.12504i	−0.341330	+	0.401594i
$29$	2.45128	−	7.54427i	0.455191	−	1.40094i	−0.415719	−	0.909493i	$-0.636470\pi$
$29$	2.45128	−	7.54427i	0.455191	−	1.40094i	0.870910	−	0.491442i	$-0.163530\pi$
$30$	−1.21965	+	2.18398i	−0.222676	+	0.398739i
$31$	−0.816325	−	1.12358i	−0.146616	−	0.201800i	0.729392	−	0.684096i	$-0.239803\pi$
$31$	−0.816325	−	1.12358i	−0.146616	−	0.201800i	−0.876008	+	0.482296i	$0.839803\pi$
$32$	4.68456	−	3.17094i	0.828121	−	0.560549i
$33$	−0.466268	+	3.28369i	−0.0811668	+	0.571616i
$34$	3.62669	+	3.91390i	0.621972	+	0.671228i
$35$	−1.44978	−	1.99544i	−0.245057	−	0.337292i
$36$	1.94361	−	0.471557i	0.323936	−	0.0785928i
$37$	8.91884	+	2.89791i	1.46625	+	0.476413i	0.929972	−	0.367630i	$-0.119831\pi$
$37$	8.91884	+	2.89791i	1.46625	+	0.476413i	0.536276	+	0.844043i	$0.319831\pi$
$38$	0.0705429	+	0.589948i	0.0114436	+	0.0957022i
$39$	−2.66400	−	1.93551i	−0.426582	−	0.309930i
$40$	1.74848	+	4.68744i	0.276460	+	0.741149i
$41$	3.29058	−	1.06918i	0.513903	−	0.166977i	−0.0405736	−	0.999177i	$-0.512919\pi$
$41$	3.29058	−	1.06918i	0.513903	−	0.166977i	0.554476	+	0.832199i	$0.312919\pi$
$42$	−0.382407	+	1.93462i	−0.0590066	+	0.298518i
$43$		−	3.60336i		−	0.549507i	−0.961515	−	0.274753i	$-0.911404\pi$
$43$		−	3.60336i		−	0.549507i	0.961515	−	0.274753i	$-0.0885962\pi$
$44$	4.40016	+	4.96373i	0.663349	+	0.748310i
$45$			1.76880i			0.263678i
$46$	−2.01086	−	0.397477i	−0.296485	−	0.0586048i
$47$	0.727433	−	0.236357i	0.106107	−	0.0344763i	−0.255482	−	0.966814i	$-0.582234\pi$
$47$	0.727433	−	0.236357i	0.106107	−	0.0344763i	0.361589	+	0.932337i	$0.382234\pi$
$48$	1.79883	−	3.57270i	0.259639	−	0.515675i
$49$	4.08999	+	2.97155i	0.584285	+	0.424508i
$50$	2.62775	−	0.314213i	0.371620	−	0.0444364i
$51$	3.58836	+	1.16593i	0.502472	+	0.163263i
$52$	−6.40011	+	1.55278i	−0.887535	+	0.215332i
$53$	−2.54374	−	3.50116i	−0.349410	−	0.480921i	0.597751	−	0.801682i	$-0.296061\pi$
$53$	−2.54374	−	3.50116i	−0.349410	−	0.480921i	−0.947160	+	0.320761i	$0.896061\pi$
$54$	1.03734	−	0.961215i	0.141164	−	0.130805i
$55$	−5.18369	+	2.74674i	−0.698969	+	0.370371i
$56$	2.45290	+	3.08856i	0.327783	+	0.412726i
$57$	0.246945	+	0.339891i	0.0327087	+	0.0450196i
$58$	−9.79446	−	5.46973i	−1.28608	−	0.718211i
$59$	3.69578	−	11.3745i	0.481150	−	1.48083i	−0.356330	−	0.934360i	$-0.615972\pi$
$59$	3.69578	−	11.3745i	0.481150	−	1.48083i	0.837480	−	0.546468i	$-0.184028\pi$
$60$	2.69552	+	2.29103i	0.347990	+	0.295770i
$61$	8.45451	+	6.14256i	1.08249	+	0.786474i	0.978115	−	0.208064i	$-0.0667163\pi$
$61$	8.45451	+	6.14256i	1.08249	+	0.786474i	0.104373	+	0.994538i	$0.466716\pi$
$62$	−1.78268	+	0.824422i	−0.226400	+	0.104702i
$63$	0.430909	+	1.32620i	0.0542894	+	0.167086i
$64$	−3.11460	−	7.36880i	−0.389325	−	0.921100i
$65$		−	5.82447i		−	0.722437i
$66$	4.42782	+	1.54739i	0.545027	+	0.190470i
$67$	9.95011			1.21560			0.607800	−	0.794090i	$-0.292052\pi$
$67$	9.95011			1.21560			0.607800	+	0.794090i	$0.292052\pi$
$68$	6.42459	−	3.95824i	0.779096	−	0.480007i
$69$	−1.37846	+	0.447890i	−0.165948	+	0.0539197i
$70$	−3.16600	+	1.46415i	−0.378409	+	0.175000i
$71$	−7.57332	+	10.4238i	−0.898788	+	1.23708i	0.0720652	+	0.997400i	$0.477041\pi$
$71$	−7.57332	+	10.4238i	−0.898788	+	1.23708i	−0.970853	+	0.239675i	$0.922959\pi$
$72$	−0.121217	−	2.82583i	−0.0142856	−	0.333027i
$73$	−9.14630	−	2.97181i	−1.07049	−	0.347824i	−0.279814	−	0.960054i	$-0.590273\pi$
$73$	−9.14630	−	2.97181i	−1.07049	−	0.347824i	−0.790680	+	0.612230i	$0.790273\pi$
$74$	6.46632	−	11.5790i	0.751695	−	1.34603i
$75$	1.51394	−	1.09994i	0.174815	−	0.127011i
$76$	0.837822	+	0.0639152i	0.0961047	+	0.00733157i
$77$	−3.21744	+	3.32227i	−0.366662	+	0.378607i
$78$	−3.41583	+	3.16518i	−0.386767	+	0.358385i
$79$	4.69761	−	3.41302i	0.528523	−	0.383994i	−0.291282	−	0.956637i	$-0.594082\pi$
$79$	4.69761	−	3.41302i	0.528523	−	0.383994i	0.819805	+	0.572643i	$0.194082\pi$
$80$	6.98271	−	1.14034i	0.780691	−	0.127493i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−0.580949	−	4.85846i	−0.0641551	−	0.536527i
$83$	−8.86730	+	12.2048i	−0.973313	+	1.33965i	−0.0329578	+	0.999457i	$0.510493\pi$
$83$	−8.86730	+	12.2048i	−0.973313	+	1.33965i	−0.940355	+	0.340194i	$0.889507\pi$
$84$	2.57916	+	1.06108i	0.281409	+	0.115773i
$85$	2.06230	+	6.34711i	0.223688	+	0.688441i
$86$	−4.99919	−	0.988166i	−0.539076	−	0.106557i
$87$	−7.93251			−0.850455
$88$	8.09320	−	4.74342i	0.862738	−	0.505651i
$89$	10.9210			1.15763			0.578814	−	0.815460i	$-0.303516\pi$
$89$	10.9210			1.15763			0.578814	+	0.815460i	$0.303516\pi$
$90$	2.45398	+	0.485067i	0.258673	+	0.0511306i
$91$	−1.41893	−	4.36703i	−0.148745	−	0.457789i
$92$	−1.10289	+	2.68080i	−0.114985	+	0.279493i
$93$	−0.816325	+	1.12358i	−0.0846490	+	0.116509i
$94$	−0.128428	−	1.07404i	−0.0132463	−	0.110778i
$95$	−0.229638	+	0.706752i	−0.0235603	+	0.0725113i
$96$	−4.46336	−	3.47541i	−0.455539	−	0.354707i
$97$	−11.2144	+	8.14771i	−1.13865	+	0.827275i	−0.986930	−	0.161149i	$-0.948480\pi$
$97$	−11.2144	+	8.14771i	−1.13865	+	0.827275i	−0.151716	+	0.988424i	$0.548480\pi$
$98$	5.24426	−	4.85943i	0.529751	−	0.490877i
$99$	3.26706	−	0.571268i	0.328351	−	0.0574146i
$100$	0.284692	−	3.73183i	0.0284692	−	0.373183i
$101$	−6.49406	+	4.71821i	−0.646183	+	0.469480i	−0.861969	−	0.506961i	$-0.830769\pi$
$101$	−6.49406	+	4.71821i	−0.646183	+	0.469480i	0.215786	+	0.976441i	$0.430769\pi$
$102$	2.60163	−	4.65865i	0.257600	−	0.461275i
$103$	11.7338	+	3.81254i	1.15617	+	0.375661i	0.823463	−	0.567370i	$-0.192039\pi$
$103$	11.7338	+	3.81254i	1.15617	+	0.375661i	0.332703	+	0.943032i	$0.392039\pi$
$104$	0.399155	+	9.30514i	0.0391403	+	0.912444i
$105$	−1.44978	+	1.99544i	−0.141484	+	0.194735i
$106$	−5.55498	+	2.56897i	−0.539548	+	0.249520i
$107$	−6.82340	+	2.21706i	−0.659643	+	0.214331i	−0.619661	−	0.784869i	$-0.712730\pi$
$107$	−6.82340	+	2.21706i	−0.659643	+	0.214331i	−0.0399817	+	0.999200i	$0.512730\pi$
$108$	−1.04909	−	1.70277i	−0.100948	−	0.163849i
$109$	−9.38007			−0.898448			−0.449224	−	0.893419i	$-0.648300\pi$
$109$	−9.38007			−0.898448			−0.449224	+	0.893419i	$0.648300\pi$
$110$	2.38920	+	7.94495i	0.227801	+	0.757522i
$111$		−	9.37782i		−	0.890103i
$112$	4.95764	−	2.55609i	0.468453	−	0.241528i
$113$	0.566005	+	1.74198i	0.0532452	+	0.163872i	0.974143	−	0.225932i	$-0.0725427\pi$
$113$	0.566005	+	1.74198i	0.0532452	+	0.163872i	−0.920898	+	0.389804i	$0.872543\pi$
$114$	0.539275	−	0.249394i	0.0505077	−	0.0233579i
$115$	−2.07408	−	1.50691i	−0.193409	−	0.140520i
$116$	−10.2745	+	12.0886i	−0.953966	+	1.12239i
$117$	−1.01756	+	3.13173i	−0.0940734	+	0.289528i
$118$	−14.7671	−	8.24669i	−1.35942	−	0.759169i
$119$	3.09251	+	4.25648i	0.283490	+	0.390191i
$120$	3.91771	−	3.11141i	0.357636	−	0.284031i
$121$	6.74753	+	8.68740i	0.613412	+	0.789763i
$122$	10.8405	−	10.0450i	0.981455	−	0.909434i
$123$	−2.03369	−	2.79914i	−0.183372	−	0.252390i
$124$	0.654905	+	2.69932i	0.0588122	+	0.242406i
$125$	11.5592	+	3.75580i	1.03388	+	0.335929i
$126$	1.95810	−	0.234139i	0.174441	−	0.0208588i
$127$	−5.77997	−	4.19940i	−0.512890	−	0.372636i	0.301029	−	0.953615i	$-0.402670\pi$
$127$	−5.77997	−	4.19940i	−0.512890	−	0.372636i	−0.813919	+	0.580979i	$0.802670\pi$
$128$	−11.0774	+	2.30032i	−0.979112	+	0.203322i
$129$	−3.42700	+	1.11350i	−0.301730	+	0.0980381i
$130$	−8.08070	−	1.59727i	−0.708724	−	0.140090i
$131$			8.74918i			0.764420i	0.924076	+	0.382210i	$0.124837\pi$
$131$			8.74918i			0.764420i	−0.924076	+	0.382210i	$0.875163\pi$
$132$	3.36106	−	5.71868i	0.292543	−	0.497747i
$133$			0.585847i			0.0507994i
$134$	2.72867	−	13.8045i	0.235721	−	1.19253i
$135$	1.68223	−	0.546590i	0.144783	−	0.0470430i
$136$	−3.72969	−	9.99877i	−0.319818	−	0.857388i
$137$	6.84644	+	4.97423i	0.584930	+	0.424977i	0.840498	−	0.541814i	$-0.182262\pi$
$137$	6.84644	+	4.97423i	0.584930	+	0.424977i	−0.255568	+	0.966791i	$0.582262\pi$
$138$	0.243367	+	2.03527i	0.0207167	+	0.173253i
$139$	−5.45350	−	1.77195i	−0.462560	−	0.150295i	0.0684604	−	0.997654i	$-0.478191\pi$
$139$	−5.45350	−	1.77195i	−0.462560	−	0.150295i	−0.531021	+	0.847359i	$0.678191\pi$
$140$	1.16310	+	4.79393i	0.0982997	+	0.405161i
$141$	−0.449578	−	0.618791i	−0.0378613	−	0.0521116i
$142$	12.3848	+	13.3656i	1.03931	+	1.12161i
$143$	−10.7581	+	1.88112i	−0.899634	+	0.157307i
$144$	−3.95371	−	0.606767i	−0.329476	−	0.0505640i
$145$	−8.24724	−	11.3514i	−0.684896	−	0.942679i
$146$	−6.63124	+	11.8743i	−0.548805	+	0.982726i
$147$	1.56224	−	4.80808i	0.128851	−	0.396563i
$148$	−14.2911	−	12.1466i	−1.17472	−	0.998440i
$149$	−15.6781	−	11.3908i	−1.28440	−	0.933168i	−0.284720	−	0.958611i	$-0.591901\pi$
$149$	−15.6781	−	11.3908i	−1.28440	−	0.933168i	−0.999676	+	0.0254423i	$0.991901\pi$
$150$	−1.11085	−	2.40204i	−0.0907009	−	0.196126i
$151$	3.22214	+	9.91672i	0.262214	+	0.807011i	0.992322	+	0.123680i	$0.0394696\pi$
$151$	3.22214	+	9.91672i	0.262214	+	0.807011i	−0.730108	+	0.683331i	$0.760530\pi$
$152$	0.318434	−	1.14484i	0.0258284	−	0.0928589i
$153$		−	3.77303i		−	0.305031i
$154$	3.72688	+	5.37486i	0.300320	+	0.433119i
$155$	−2.45654			−0.197314
$156$	3.45453	+	5.60703i	0.276584	+	0.448921i
$157$	−16.9246	+	5.49914i	−1.35073	+	0.438879i	−0.892938	−	0.450180i	$-0.851360\pi$
$157$	−16.9246	+	5.49914i	−1.35073	+	0.438879i	−0.457792	+	0.889059i	$0.651360\pi$
$158$	−3.44687	−	7.45330i	−0.274218	−	0.592952i
$159$	−2.54374	+	3.50116i	−0.201732	+	0.277660i
$160$	0.332834	−	10.0003i	0.0263128	−	0.790595i
$161$	−1.92220	−	0.624560i	−0.151491	−	0.0492223i
$162$	−1.23472	−	0.689534i	−0.0970091	−	0.0541749i
$163$	−4.84269	+	3.51842i	−0.379308	+	0.275584i	−0.761060	−	0.648681i	$-0.775321\pi$
$163$	−4.84269	+	3.51842i	−0.379308	+	0.275584i	0.381752	+	0.924265i	$0.375321\pi$
$164$	−6.89980	−	0.526367i	−0.538784	−	0.0411024i
$165$	4.21416	+	4.08119i	0.328072	+	0.317721i
$166$	14.5008	+	15.6492i	1.12548	+	1.21461i
$167$	−4.20600	+	3.05584i	−0.325470	+	0.236468i	−0.738506	−	0.674247i	$-0.764468\pi$
$167$	−4.20600	+	3.05584i	−0.325470	+	0.236468i	0.413036	+	0.910715i	$0.364468\pi$
$168$	2.17940	−	3.28727i	0.168145	−	0.253618i
$169$	−0.666510	+	2.05131i	−0.0512700	+	0.157793i
$170$	9.37134	−	1.12058i	0.718749	−	0.0859442i
$171$	0.246945	−	0.339891i	0.0188844	−	0.0259921i
$172$	−2.74190	+	6.66473i	−0.209068	+	0.508181i
$173$	−4.33891	−	13.3538i	−0.329881	−	1.01527i	−0.969189	−	0.246319i	$-0.920779\pi$
$173$	−4.33891	−	13.3538i	−0.329881	−	1.01527i	0.639307	−	0.768951i	$-0.279221\pi$
$174$	−2.17537	+	11.0053i	−0.164914	+	0.834312i
$175$	2.60949			0.197259
$176$	−4.36145	−	12.5291i	−0.328756	−	0.944415i
$177$	−11.9598			−0.898954
$178$	2.99493	−	15.1515i	0.224479	−	1.13565i
$179$	7.11085	+	21.8849i	0.531490	+	1.63576i	0.751114	+	0.660173i	$0.229517\pi$
$179$	7.11085	+	21.8849i	0.531490	+	1.63576i	−0.219624	+	0.975585i	$0.570483\pi$
$180$	1.34594	−	3.27156i	0.100320	−	0.243848i
$181$	11.4700	−	15.7871i	0.852559	−	1.17345i	−0.130734	−	0.991418i	$-0.541733\pi$
$181$	11.4700	−	15.7871i	0.852559	−	1.17345i	0.983293	−	0.182030i	$-0.0582668\pi$
$182$	−6.44781	+	0.770995i	−0.477944	+	0.0571500i
$183$	3.22933	−	9.93887i	0.238719	−	0.734702i
$184$	3.41681	+	2.26529i	0.251891	+	0.167000i
$185$	13.4196	−	9.74989i	0.986627	−	0.716827i
$186$	1.33495	+	1.44067i	0.0978833	+	0.105635i
$187$	11.0573	−	5.85908i	0.808592	−	0.428458i
$188$	−1.52530	−	0.116361i	−0.111244	−	0.00848653i
$189$	1.12813	−	0.819637i	0.0820596	−	0.0596198i
$190$	0.917552	+	0.512409i	0.0665663	+	0.0371740i
$191$	24.3481	+	7.91117i	1.76177	+	0.572432i	0.997381	−	0.0723280i	$-0.0230428\pi$
$191$	24.3481	+	7.91117i	1.76177	+	0.572432i	0.764385	+	0.644760i	$0.223043\pi$
$192$	−6.04568	+	5.23925i	−0.436310	+	0.378110i
$193$	12.9917	−	17.8816i	0.935166	−	1.28715i	−0.0226438	−	0.999744i	$-0.507208\pi$
$193$	12.9917	−	17.8816i	0.935166	−	1.28715i	0.957810	−	0.287402i	$-0.0927917\pi$
$194$	8.22852	+	17.7929i	0.590774	+	1.27745i
$195$	−5.53940	+	1.79986i	−0.396685	+	0.128891i
$196$	−5.30367	−	8.60836i	−0.378834	−	0.614883i
$197$	−18.2227			−1.29832			−0.649158	−	0.760653i	$-0.724879\pi$
$197$	−18.2227			−1.29832			−0.649158	+	0.760653i	$0.724879\pi$
$198$	0.103381	−	4.68928i	0.00734693	−	0.333252i
$199$		−	13.2643i		−	0.940284i	−0.882591	−	0.470142i	$-0.844203\pi$
$199$		−	13.2643i		−	0.940284i	0.882591	−	0.470142i	$-0.155797\pi$
$200$	−5.09936	−	1.41837i	−0.360579	−	0.100294i
$201$	−3.07475	−	9.46312i	−0.216876	−	0.667477i
$202$	4.76501	+	10.3036i	0.335265	+	0.724956i
$203$	−8.94893	−	6.50178i	−0.628092	−	0.456335i
$204$	−5.74981	−	4.88699i	−0.402567	−	0.342158i
$205$	1.89116	−	5.82039i	0.132084	−	0.406514i
$206$	8.50723	−	15.2336i	0.592727	−	1.06137i
$207$	0.851938	+	1.17259i	0.0592138	+	0.0815008i
$208$	13.0191	+	1.99802i	0.902715	+	0.138538i
$209$	1.37957	+	0.195892i	0.0954268	+	0.0135501i
$210$	2.37084	+	2.55860i	0.163604	+	0.176560i
$211$	11.2460	+	15.4787i	0.774204	+	1.06560i	0.995898	+	0.0904841i	$0.0288414\pi$
$211$	11.2460	+	15.4787i	0.774204	+	1.06560i	−0.221694	+	0.975116i	$0.571159\pi$
$212$	2.04074	+	8.41132i	0.140159	+	0.577692i
$213$	12.2539	+	3.98153i	0.839623	+	0.272810i
$214$	1.20466	+	10.0746i	0.0823492	+	0.688684i
$215$	−5.15637	−	3.74632i	−0.351662	−	0.255497i
$216$	−2.65006	+	0.988513i	−0.180314	+	0.0672598i
$217$	−1.84185	+	0.598452i	−0.125033	+	0.0406256i
$218$	−2.57234	+	13.0136i	−0.174221	+	0.881394i
$219$			9.61699i			0.649856i
$220$	11.6778	−	1.13592i	0.787317	−	0.0765840i
$221$			12.4242i			0.835740i
$222$	−13.0105	−	2.57172i	−0.873208	−	0.172603i
$223$	1.64768	−	0.535364i	0.110337	−	0.0358507i	−0.253328	−	0.967380i	$-0.581525\pi$
$223$	1.64768	−	0.535364i	0.110337	−	0.0358507i	0.363665	+	0.931530i	$0.381525\pi$
$224$	−2.18669	−	7.57905i	−0.146104	−	0.506397i
$225$	−1.51394	−	1.09994i	−0.100930	−	0.0733296i
$226$	2.57199	−	0.307545i	0.171086	−	0.0204576i
$227$	5.99045	+	1.94642i	0.397600	+	0.129188i	0.500991	−	0.865453i	$-0.332969\pi$
$227$	5.99045	+	1.94642i	0.397600	+	0.129188i	−0.103390	+	0.994641i	$0.532969\pi$
$228$	−0.198114	−	0.816567i	−0.0131204	−	0.0540784i
$229$	2.03611	+	2.80246i	0.134550	+	0.185192i	0.870975	−	0.491327i	$-0.163488\pi$
$229$	2.03611	+	2.80246i	0.134550	+	0.185192i	−0.736426	+	0.676519i	$0.763488\pi$
$230$	−2.65943	+	2.46427i	−0.175357	+	0.162489i
$231$	4.15391	+	2.03333i	0.273307	+	0.133783i
$232$	13.9537	+	17.5697i	0.916103	+	1.15351i
$233$	−8.63879	−	11.8903i	−0.565946	−	0.778958i	0.426121	−	0.904666i	$-0.359880\pi$
$233$	−8.63879	−	11.8903i	−0.565946	−	0.778958i	−0.992067	+	0.125708i	$0.959880\pi$
$234$	4.06581	+	2.27056i	0.265790	+	0.148431i
$235$	0.418069	−	1.28669i	0.0272718	−	0.0839341i
$236$	−15.4909	+	18.2259i	−1.00837	+	1.18640i
$237$	−4.69761	−	3.41302i	−0.305143	−	0.221699i
$238$	6.75339	−	3.12319i	0.437757	−	0.202446i
$239$	6.25422	+	19.2485i	0.404552	+	1.24508i	0.921269	+	0.388927i	$0.127154\pi$
$239$	6.25422	+	19.2485i	0.404552	+	1.24508i	−0.516717	+	0.856156i	$0.672846\pi$
$240$	−3.24230	−	6.28857i	−0.209290	−	0.405925i
$241$		−	8.76302i		−	0.564476i	−0.959344	−	0.282238i	$-0.908923\pi$
$241$		−	8.76302i		−	0.564476i	0.959344	−	0.282238i	$-0.0910768\pi$
$242$	13.9030	−	6.97893i	0.893721	−	0.448623i
$243$	−1.00000			−0.0641500
$244$	−10.9633	−	17.7945i	−0.701854	−	1.13918i
$245$	8.50454	−	2.76329i	0.543335	−	0.176540i
$246$	−4.44115	+	2.05386i	−0.283157	+	0.130950i
$247$	−0.813163	+	1.11922i	−0.0517403	+	0.0712145i
$248$	3.92455	−	0.168348i	0.249209	−	0.0106901i
$249$	14.3476	+	4.66182i	0.909242	+	0.295431i
$250$	8.38062	−	15.0069i	0.530037	−	0.949119i
$251$	−4.24381	+	3.08331i	−0.267867	+	0.194617i	−0.713608	−	0.700545i	$-0.752940\pi$
$251$	−4.24381	+	3.08331i	−0.267867	+	0.194617i	0.445741	+	0.895162i	$0.352940\pi$
$252$	0.212141	−	2.78082i	0.0133636	−	0.175175i
$253$	−2.11346	+	4.31761i	−0.132872	+	0.271446i
$254$	−7.41118	+	6.86734i	−0.465019	+	0.430895i
$255$	5.39917	−	3.92273i	0.338109	−	0.245651i
$256$	0.153595	+	15.9993i	0.00959968	+	0.999954i
$257$	−1.45063	+	4.46459i	−0.0904879	+	0.278493i	−0.986052	−	0.166440i	$-0.946773\pi$
$257$	−1.45063	+	4.46459i	−0.0904879	+	0.278493i	0.895564	+	0.444933i	$0.146773\pi$
$258$	0.605033	+	5.05987i	0.0376677	+	0.315014i
$259$	7.68641	−	10.5794i	0.477610	−	0.657374i
$260$	−4.43202	+	10.7729i	−0.274862	+	0.668106i
$261$	2.45128	+	7.54427i	0.151730	+	0.466978i
$262$	12.1384	+	2.39933i	0.749910	+	0.148231i
$263$	23.0463			1.42110			0.710548	−	0.703648i	$-0.248447\pi$
$263$	23.0463			1.42110			0.710548	+	0.703648i	$0.248447\pi$
$264$	−7.01220	−	6.23129i	−0.431571	−	0.383510i
$265$	−7.65479			−0.470230
$266$	0.812787	+	0.160660i	0.0498352	+	0.00985068i
$267$	−3.37479	−	10.3865i	−0.206534	−	0.635645i
$268$	−18.4036	−	7.57134i	−1.12418	−	0.462493i
$269$	5.66339	−	7.79498i	0.345303	−	0.475268i	−0.600678	−	0.799491i	$-0.705103\pi$
$269$	5.66339	−	7.79498i	0.345303	−	0.475268i	0.945981	+	0.324223i	$0.105103\pi$
$270$	−0.296996	−	2.48377i	−0.0180746	−	0.151157i
$271$	7.25330	−	22.3234i	0.440607	−	1.35605i	−0.446624	−	0.894722i	$-0.647374\pi$
$271$	7.25330	−	22.3234i	0.440607	−	1.35605i	0.887230	−	0.461326i	$-0.152626\pi$
$272$	−14.8948	+	2.43245i	−0.903130	+	0.147489i
$273$	−3.71482	+	2.69897i	−0.224831	+	0.163349i
$274$	8.77862	−	8.13443i	0.530336	−	0.491419i
$275$	0.872544	−	6.14489i	0.0526164	−	0.370551i
$276$	2.89041	+	0.220502i	0.173982	+	0.0132726i
$277$	−16.1312	+	11.7200i	−0.969227	+	0.704185i	−0.955275	−	0.295718i	$-0.904441\pi$
$277$	−16.1312	+	11.7200i	−0.969227	+	0.704185i	−0.0139521	+	0.999903i	$0.504441\pi$
$278$	−3.95389	+	7.08010i	−0.237139	+	0.424636i
$279$	1.32084	+	0.429168i	0.0790767	+	0.0256936i
$280$	6.96992	−	0.298983i	0.416532	−	0.0178676i
$281$	−3.73754	+	5.14428i	−0.222963	+	0.306882i	−0.905814	−	0.423675i	$-0.860740\pi$
$281$	−3.73754	+	5.14428i	−0.222963	+	0.306882i	0.682851	+	0.730557i	$0.260740\pi$
$282$	−0.981783	+	0.454037i	−0.0584643	+	0.0270375i
$283$	−8.30006	+	2.69685i	−0.493387	+	0.160311i	−0.545134	−	0.838349i	$-0.683521\pi$
$283$	−8.30006	+	2.69685i	−0.493387	+	0.160311i	0.0517465	+	0.998660i	$0.483521\pi$
$284$	21.9393	−	13.5170i	1.30186	−	0.802084i
$285$	0.743124			0.0440188
$286$	−0.340421	+	15.4413i	−0.0201295	+	0.913062i
$287$		−	4.82469i		−	0.284792i
$288$	−1.92606	+	5.31886i	−0.113494	+	0.313417i
$289$	0.854199	+	2.62895i	0.0502470	+	0.154644i
$290$	−18.0102	+	8.32904i	−1.05760	+	0.489098i
$291$	11.2144	+	8.14771i	0.657398	+	0.477627i
$292$	14.6556	+	12.4563i	0.857652	+	0.728952i
$293$	6.37463	−	19.6191i	0.372410	−	1.14616i	−0.572799	−	0.819696i	$-0.694143\pi$
$293$	6.37463	−	19.6191i	0.372410	−	1.14616i	0.945209	−	0.326465i	$-0.105857\pi$
$294$	−6.24216	−	3.48594i	−0.364050	−	0.203304i
$295$	−12.4343	−	17.1144i	−0.723955	−	0.996438i
$296$	−20.7709	+	16.4960i	−1.20728	+	0.958812i
$297$	−1.55288	−	2.93062i	−0.0901075	−	0.170052i
$298$	−20.1027	+	18.6275i	−1.16452	+	1.07906i
$299$	−2.80534	−	3.86122i	−0.162237	−	0.223300i
$300$	−3.63716	+	0.882442i	−0.209991	+	0.0509478i
$301$	−4.77877	−	1.55272i	−0.275444	−	0.0894971i
$302$	14.6418	−	1.75079i	0.842540	−	0.100746i
$303$	6.49406	+	4.71821i	0.373074	+	0.271054i
$304$	−1.50099	−	0.755741i	−0.0860878	−	0.0433447i
$305$	17.5799	−	5.71205i	1.00662	−	0.327071i
$306$	−5.23459	−	1.03470i	−0.299241	−	0.0591496i
$307$			24.6574i			1.40727i	0.710560	+	0.703637i	$0.248442\pi$
$307$			24.6574i			1.40727i	−0.710560	+	0.703637i	$0.751558\pi$
$308$	8.47896	−	3.69658i	0.483134	−	0.210632i
$309$		−	12.3377i		−	0.701864i
$310$	−0.673669	+	3.40813i	−0.0382618	+	0.193569i
$311$	24.3504	−	7.91194i	1.38079	−	0.448645i	0.477859	−	0.878437i	$-0.341413\pi$
$311$	24.3504	−	7.91194i	1.38079	−	0.448645i	0.902928	+	0.429792i	$0.141413\pi$
$312$	8.72637	−	3.25507i	0.494034	−	0.184282i
$313$	3.15731	+	2.29392i	0.178462	+	0.129660i	0.673430	−	0.739251i	$-0.264820\pi$
$313$	3.15731	+	2.29392i	0.178462	+	0.129660i	−0.494968	+	0.868911i	$0.664820\pi$
$314$	2.98802	+	24.9887i	0.168624	+	1.41020i
$315$	2.34579	+	0.762192i	0.132170	+	0.0429447i
$316$	−11.2857	+	2.73813i	−0.634872	+	0.154032i
$317$	3.74958	+	5.16085i	0.210597	+	0.289862i	0.901228	−	0.433345i	$-0.142667\pi$
$317$	3.74958	+	5.16085i	0.210597	+	0.289862i	−0.690631	+	0.723208i	$0.742667\pi$
$318$	4.15982	+	4.48925i	0.233271	+	0.251745i
$319$	−18.3028	+	18.8991i	−1.02476	+	1.05815i
$320$	−13.7829	−	3.20420i	−0.770486	−	0.179120i
$321$	4.21709	+	5.80433i	0.235375	+	0.323966i
$322$	−1.39363	+	2.49553i	−0.0776640	+	0.139070i
$323$	0.489840	−	1.50757i	0.0272554	−	0.0838836i
$324$	−1.29524	+	1.52392i	−0.0719579	+	0.0846625i
$325$	4.98525	+	3.62200i	0.276532	+	0.200912i
$326$	3.55331	+	7.68347i	0.196800	+	0.425548i
$327$	2.89860	+	8.92098i	0.160293	+	0.493331i
$328$	−2.62243	+	9.42823i	−0.144800	+	0.520587i
$329$		−	1.06657i		−	0.0588019i
$330$	6.81780	−	4.72739i	0.375307	−	0.260234i
$331$	−4.34773			−0.238973			−0.119486	−	0.992836i	$-0.538125\pi$
$331$	−4.34773			−0.238973			−0.119486	+	0.992836i	$0.538125\pi$
$332$	25.6879	−	15.8265i	1.40981	−	0.868591i
$333$	−8.91884	+	2.89791i	−0.488749	+	0.158804i
$334$	3.08615	+	6.67330i	0.168867	+	0.365147i
$335$	10.3449	−	14.2385i	0.565202	−	0.777934i
$336$	−3.96298	−	3.92512i	−0.216199	−	0.214133i
$337$	9.71778	+	3.15750i	0.529361	+	0.172000i	0.561490	−	0.827484i	$-0.310229\pi$
$337$	9.71778	+	3.15750i	0.529361	+	0.172000i	−0.0321283	+	0.999484i	$0.510229\pi$
$338$	2.66314	+	1.48723i	0.144856	+	0.0808949i
$339$	1.48182	−	1.07660i	0.0804814	−	0.0584731i
$340$	1.01529	−	13.3088i	0.0550621	−	0.721772i
$341$	0.793386	+	4.53734i	0.0429642	+	0.245711i
$342$	−0.403833	−	0.435814i	−0.0218368	−	0.0235661i
$343$	13.6002	−	9.88114i	0.734343	−	0.533531i
$344$	8.49453	+	5.63173i	0.457994	+	0.303643i
$345$	−0.792229	+	2.43823i	−0.0426522	+	0.131270i
$346$	−19.7165	+	2.35760i	−1.05997	+	0.126745i
$347$	4.37155	−	6.01692i	0.234677	−	0.323005i	−0.675394	−	0.737457i	$-0.736027\pi$
$347$	4.37155	−	6.01692i	0.234677	−	0.323005i	0.910071	+	0.414452i	$0.136027\pi$
$348$	14.6719	+	6.03609i	0.786496	+	0.323568i
$349$	−1.81469	−	5.58504i	−0.0971382	−	0.298961i	0.890667	−	0.454657i	$-0.150238\pi$
$349$	−1.81469	−	5.58504i	−0.0971382	−	0.298961i	−0.987805	+	0.155696i	$0.950238\pi$
$350$	0.715612	−	3.62032i	0.0382511	−	0.193514i
$351$	3.29289			0.175762
$352$	−18.5785	+	2.61503i	−0.990239	+	0.139382i
$353$	−26.3624			−1.40313			−0.701565	−	0.712605i	$-0.747515\pi$
$353$	−26.3624			−1.40313			−0.701565	+	0.712605i	$0.747515\pi$
$354$	−3.27980	+	16.5927i	−0.174319	+	0.881891i
$355$	7.04254	+	21.6747i	0.373779	+	1.15037i
$356$	−20.1995	−	8.31015i	−1.07057	−	0.440437i
$357$	3.09251	−	4.25648i	0.163673	−	0.225277i
$358$	32.3126	−	3.86377i	1.70777	−	0.204206i
$359$	1.23260	−	3.79354i	0.0650539	−	0.200215i	−0.913246	−	0.407408i	$-0.866433\pi$
$359$	1.23260	−	3.79354i	0.0650539	−	0.200215i	0.978300	+	0.207193i	$0.0664327\pi$
$360$	−4.16976	−	2.76449i	−0.219766	−	0.145701i
$361$	−15.2285	+	11.0642i	−0.801501	+	0.582325i
$362$	−18.7571	−	20.2425i	−0.985851	−	1.06392i
$363$	6.17710	−	9.10183i	0.324214	−	0.477722i
$364$	−0.698558	+	9.15693i	−0.0366144	+	0.479954i
$365$	−13.7618	+	9.99855i	−0.720327	+	0.523348i
$366$	−12.9033	−	7.20586i	−0.674466	−	0.376657i
$367$	−31.5697	−	10.2576i	−1.64792	−	0.535443i	−0.669634	−	0.742691i	$-0.733549\pi$
$367$	−31.5697	−	10.2576i	−1.64792	−	0.535443i	−0.978288	+	0.207248i	$0.933549\pi$
$368$	4.07981	−	4.11916i	0.212675	−	0.214726i
$369$	−2.03369	+	2.79914i	−0.105870	+	0.145717i
$370$	−9.84660	−	21.2917i	−0.511900	−	1.10690i
$371$	−5.73936	+	1.86483i	−0.297973	+	0.0968171i
$372$	2.36483	−	1.45699i	0.122611	−	0.0755413i
$373$	−30.7237			−1.59081			−0.795407	−	0.606075i	$-0.792743\pi$
$373$	−30.7237			−1.59081			−0.795407	+	0.606075i	$0.792743\pi$
$374$	−5.09640	−	16.9474i	−0.263529	−	0.876327i
$375$		−	12.1540i		−	0.627632i
$376$	−0.579728	+	2.08425i	−0.0298972	+	0.107487i
$377$	−8.07180	−	24.8424i	−0.415719	−	1.27945i
$378$	−0.827766	−	1.78991i	−0.0425757	−	0.0920631i
$379$	−29.7001	−	21.5784i	−1.52559	−	1.10841i	−0.958626	−	0.284667i	$-0.908117\pi$
$379$	−29.7001	−	21.5784i	−1.52559	−	1.10841i	−0.566967	−	0.823741i	$-0.691883\pi$
$380$	0.962525	−	1.13246i	0.0493765	−	0.0580942i
$381$	−2.20775	+	6.79476i	−0.113107	+	0.348106i
$382$	17.6528	−	31.6103i	0.903197	−	1.61732i
$383$	−7.33813	−	10.1001i	−0.374961	−	0.516090i	0.579280	−	0.815129i	$-0.303334\pi$
$383$	−7.33813	−	10.1001i	−0.374961	−	0.516090i	−0.954241	+	0.299039i	$0.903334\pi$
$384$	5.61084	+	9.82438i	0.286327	+	0.501348i
$385$	1.40904	+	8.05821i	0.0718111	+	0.410684i
$386$	−21.2456	−	22.9281i	−1.08137	−	1.16701i
$387$	2.11800	+	2.91518i	0.107664	+	0.148187i
$388$	26.9418	−	6.53659i	1.36776	−	0.331845i
$389$	31.6936	+	10.2979i	1.60693	+	0.522122i	0.968807	−	0.247815i	$-0.0797124\pi$
$389$	31.6936	+	10.2979i	1.60693	+	0.522122i	0.638120	+	0.769937i	$0.279712\pi$
$390$	0.977976	+	8.17879i	0.0495218	+	0.414149i
$391$	4.42422	+	3.21439i	0.223743	+	0.162559i
$392$	−13.3974	+	4.99744i	−0.676672	+	0.252409i
$393$	8.32097	−	2.70365i	0.419737	−	0.136381i
$394$	−4.99731	+	25.2817i	−0.251761	+	1.27367i
$395$		−	10.2707i		−	0.516774i
$396$	−6.47741	−	1.42939i	−0.325502	−	0.0718295i
$397$		−	14.1022i		−	0.707767i	−0.935289	−	0.353884i	$-0.884861\pi$
$397$		−	14.1022i		−	0.707767i	0.935289	−	0.353884i	$-0.115139\pi$
$398$	−18.4025	−	3.63754i	−0.922436	−	0.182334i
$399$	0.557174	−	0.181037i	0.0278936	−	0.00906317i
$400$	−3.36623	+	6.68573i	−0.168311	+	0.334287i
$401$	9.67496	+	7.02927i	0.483145	+	0.351025i	0.802542	−	0.596596i	$-0.203480\pi$
$401$	9.67496	+	7.02927i	0.483145	+	0.351025i	−0.319397	+	0.947621i	$0.603480\pi$
$402$	−13.9721	+	1.67070i	−0.696863	+	0.0833272i
$403$	−4.34939	−	1.41320i	−0.216658	−	0.0703966i
$404$	15.6016	−	3.78523i	0.776208	−	0.188322i
$405$	−1.03968	−	1.43099i	−0.0516619	−	0.0711065i
$406$	−11.4745	+	10.6325i	−0.569469	+	0.527680i
$407$	−22.3426	−	21.6376i	−1.10748	−	1.07254i
$408$	−8.35686	+	6.63694i	−0.413726	+	0.328577i
$409$	−9.59791	−	13.2104i	−0.474586	−	0.653212i	0.502867	−	0.864364i	$-0.332279\pi$
$409$	−9.59791	−	13.2104i	−0.474586	−	0.653212i	−0.977453	+	0.211152i	$0.932279\pi$
$410$	−7.55642	−	4.21989i	−0.373185	−	0.208406i
$411$	2.61511	−	8.04847i	0.128994	−	0.397002i
$412$	−18.8017	−	15.9803i	−0.926291	−	0.787290i
$413$	−13.4923	−	9.80270i	−0.663911	−	0.482359i
$414$	1.86045	−	0.860388i	0.0914361	−	0.0422857i
$415$	8.24584	+	25.3781i	0.404772	+	1.24576i
$416$	6.34229	−	17.5144i	0.310956	−	0.858716i
$417$			5.73415i			0.280803i
$418$	0.650101	−	1.86025i	0.0317975	−	0.0909879i
$419$	5.36954			0.262319			0.131159	−	0.991361i	$-0.458130\pi$
$419$	5.36954			0.262319			0.131159	+	0.991361i	$0.458130\pi$
$420$	4.19989	−	2.58758i	0.204933	−	0.126261i
$421$	−8.90313	+	2.89280i	−0.433912	+	0.140987i	−0.517825	−	0.855487i	$-0.673258\pi$
$421$	−8.90313	+	2.89280i	−0.433912	+	0.140987i	0.0839132	+	0.996473i	$0.473258\pi$
$422$	24.5588	−	11.3575i	1.19550	−	0.552875i
$423$	−0.449578	+	0.618791i	−0.0218592	+	0.0300867i
$424$	12.2293	−	0.524588i	0.593905	−	0.0254762i
$425$	−6.71504	−	2.18185i	−0.325727	−	0.105835i
$426$	8.88430	−	15.9088i	0.430446	−	0.770784i
$427$	11.7894	−	8.56549i	0.570528	−	0.414513i
$428$	14.3075	+	1.09148i	0.691580	+	0.0527588i
$429$	5.11348	+	9.65022i	0.246881	+	0.465917i
$430$	−6.61159	+	6.12642i	−0.318839	+	0.295442i
$431$	−30.9429	+	22.4813i	−1.49047	+	1.08289i	−0.516477	+	0.856301i	$0.672757\pi$
$431$	−30.9429	+	22.4813i	−1.49047	+	1.08289i	−0.973991	+	0.226587i	$0.927243\pi$
$432$	0.644694	+	3.94770i	0.0310178	+	0.189934i
$433$	3.07438	−	9.46196i	0.147745	−	0.454713i	−0.849609	−	0.527414i	$-0.823162\pi$
$433$	3.07438	−	9.46196i	0.147745	−	0.454713i	0.997354	+	0.0727008i	$0.0231618\pi$
$434$	0.325176	+	2.71944i	0.0156090	+	0.130537i
$435$	−8.24724	+	11.3514i	−0.395425	+	0.544256i
$436$	17.3493	+	7.13758i	0.830881	+	0.341828i
$437$	0.188171	+	0.579132i	0.00900145	+	0.0277036i
$438$	13.3423	+	2.63731i	0.637521	+	0.126016i
$439$	−15.8844			−0.758122			−0.379061	−	0.925372i	$-0.623753\pi$
$439$	−15.8844			−0.758122			−0.379061	+	0.925372i	$0.623753\pi$
$440$	1.62651	−	16.5129i	0.0775408	−	0.787223i
$441$	−5.05551			−0.240739
$442$	17.2369	+	3.40714i	0.819877	+	0.162061i
$443$	−1.67612	−	5.15857i	−0.0796349	−	0.245091i	0.903311	−	0.428986i	$-0.141129\pi$
$443$	−1.67612	−	5.15857i	−0.0796349	−	0.245091i	−0.982946	+	0.183895i	$0.941129\pi$
$444$	−7.13587	+	17.3451i	−0.338653	+	0.823163i
$445$	11.3543	−	15.6279i	0.538247	−	0.740834i
$446$	−0.290897	−	2.43276i	−0.0137744	−	0.115195i
$447$	−5.98848	+	18.4307i	−0.283246	+	0.871740i
$448$	−11.1146	+	0.955306i	−0.525116	+	0.0451340i
$449$	−8.05234	+	5.85037i	−0.380013	+	0.276096i	−0.761351	−	0.648340i	$-0.775464\pi$
$449$	−8.05234	+	5.85037i	−0.380013	+	0.276096i	0.381338	+	0.924436i	$0.375464\pi$
$450$	−1.94121	+	1.79876i	−0.0915093	+	0.0847942i
$451$	−11.3613	−	1.61325i	−0.534983	−	0.0759650i
$452$	0.278651	−	3.65264i	0.0131066	−	0.171806i
$453$	8.43566	−	6.12887i	0.396342	−	0.287959i
$454$	4.34319	−	7.77720i	0.203836	−	0.365002i
$455$	−7.72442	−	2.50982i	−0.362126	−	0.117662i
$456$	−1.18721	+	0.0509267i	−0.0555962	+	0.00238486i
$457$	−14.7492	+	20.3005i	−0.689939	+	0.949619i	−0.999999	−	0.00109777i	$-0.999651\pi$
$457$	−14.7492	+	20.3005i	−0.689939	+	0.949619i	0.310061	+	0.950717i	$0.399651\pi$
$458$	4.44643	−	2.05630i	0.207768	−	0.0960848i
$459$	−3.58836	+	1.16593i	−0.167491	+	0.0544210i
$460$	2.68955	+	4.36540i	0.125401	+	0.203538i
$461$	34.5074			1.60717			0.803585	−	0.595190i	$-0.202923\pi$
$461$	34.5074			1.60717			0.803585	+	0.595190i	$0.202923\pi$
$462$	3.96013	−	5.20539i	0.184242	−	0.242177i
$463$			22.7879i			1.05905i	0.848296	+	0.529523i	$0.177629\pi$
$463$			22.7879i			1.05905i	−0.848296	+	0.529523i	$0.822371\pi$
$464$	28.2022	−	14.5407i	1.30925	−	0.675034i
$465$	0.759113	+	2.33631i	0.0352030	+	0.108344i
$466$	−18.8653	+	8.72447i	−0.873917	+	0.404153i
$467$	4.94788	+	3.59484i	0.228960	+	0.166349i	0.696351	−	0.717702i	$-0.254806\pi$
$467$	4.94788	+	3.59484i	0.228960	+	0.166349i	−0.467390	+	0.884051i	$0.654806\pi$
$468$	4.26509	−	5.01812i	0.197154	−	0.231963i
$469$	4.28759	−	13.1958i	0.197982	−	0.609327i
$470$	−1.67046	−	0.932871i	−0.0770525	−	0.0430301i
$471$	10.4600	+	14.3969i	0.481970	+	0.663375i
$472$	21.0379	+	26.4897i	0.968346	+	1.21929i
$473$	−5.25428	+	10.7340i	−0.241592	+	0.493549i
$474$	−6.02336	+	5.58136i	−0.276662	+	0.256360i
$475$	−0.462118	−	0.636050i	−0.0212034	−	0.0291840i
$476$	−2.48100	−	10.2259i	−0.113716	−	0.468705i
$477$	4.11586	+	1.33732i	0.188452	+	0.0612318i
$478$	28.4199	−	3.39831i	1.29990	−	0.155435i
$479$	−2.50936	−	1.82316i	−0.114656	−	0.0833022i	0.528980	−	0.848634i	$-0.322575\pi$
$479$	−2.50936	−	1.82316i	−0.114656	−	0.0833022i	−0.643635	+	0.765332i	$0.722575\pi$
$480$	−9.61372	+	2.77373i	−0.438804	+	0.126603i
$481$	29.3688	−	9.54249i	1.33910	−	0.435100i
$482$	−12.1576	−	2.40313i	−0.553762	−	0.109459i
$483$			2.02112i			0.0919641i
$484$	−5.86966	−	21.2025i	−0.266803	−	0.963751i
$485$			24.5186i			1.11333i
$486$	−0.274235	+	1.38737i	−0.0124395	+	0.0629324i
$487$	−20.1262	+	6.53939i	−0.912003	+	0.296328i	−0.727182	−	0.686444i	$-0.759171\pi$
$487$	−20.1262	+	6.53939i	−0.912003	+	0.296328i	−0.184821	+	0.982772i	$0.559171\pi$
$488$	−27.6941	+	10.3303i	−1.25365	+	0.467631i
$489$	4.84269	+	3.51842i	0.218994	+	0.159108i
$490$	−1.50147	−	12.5567i	−0.0678294	−	0.567255i
$491$	−4.96607	−	1.61357i	−0.224116	−	0.0728195i	0.194807	−	0.980842i	$-0.437592\pi$
$491$	−4.96607	−	1.61357i	−0.224116	−	0.0728195i	−0.418922	+	0.908022i	$0.637592\pi$
$492$	1.63155	+	6.72476i	0.0735560	+	0.303175i
$493$	17.5922	+	24.2136i	0.792312	+	1.09052i
$494$	1.32978	+	1.43509i	0.0598296	+	0.0645677i
$495$	2.57920	−	5.26906i	0.115926	−	0.236827i
$496$	0.842688	−	5.49098i	0.0378378	−	0.246552i
$497$	10.5606	+	14.5354i	0.473708	+	0.652003i
$498$	10.4023	−	18.6270i	0.466137	−	0.834696i
$499$	−9.84802	+	30.3091i	−0.440858	+	1.35682i	0.446105	+	0.894980i	$0.352811\pi$
$499$	−9.84802	+	30.3091i	−0.440858	+	1.35682i	−0.886963	+	0.461840i	$0.847189\pi$
$500$	−18.5218	−	15.7424i	−0.828322	−	0.704023i
$501$	4.20600	+	3.05584i	0.187910	+	0.136525i
$502$	3.11389	+	6.73328i	0.138980	+	0.300521i
$503$	4.38495	+	13.4955i	0.195515	+	0.601734i	0.999970	+	0.00772063i	$0.00245758\pi$
$503$	4.38495	+	13.4955i	0.195515	+	0.601734i	−0.804455	+	0.594014i	$0.797542\pi$
$504$	−3.79985	−	1.05692i	−0.169259	−	0.0470788i
$505$			14.1984i			0.631819i
$506$	5.41053	+	4.11620i	0.240528	+	0.182987i
$507$	2.15687			0.0957900
$508$	7.49513	+	12.1653i	0.332543	+	0.539749i
$509$	8.45834	−	2.74828i	0.374909	−	0.121815i	−0.115500	−	0.993307i	$-0.536847\pi$
$509$	8.45834	−	2.74828i	0.374909	−	0.121815i	0.490410	+	0.871492i	$0.336847\pi$
$510$	−3.96163	−	8.56640i	−0.175424	−	0.379326i
$511$	−7.88244	+	10.8492i	−0.348699	+	0.479942i
$512$	22.2390	+	4.17446i	0.982835	+	0.184487i
$513$	−0.399566	−	0.129827i	−0.0176412	−	0.00573199i
$514$	5.79622	+	3.23691i	0.255660	+	0.142774i
$515$	17.6551	−	12.8272i	0.777975	−	0.565232i
$516$	7.18583	+	0.548188i	0.316339	+	0.0241326i
$517$	−2.51159	−	0.356633i	−0.110459	−	0.0156847i
$518$	−12.5697	−	13.5651i	−0.552281	−	0.596018i
$519$	−11.3594	+	8.25310i	−0.498623	+	0.362271i
$520$	13.7306	+	9.10315i	0.602125	+	0.399199i
$521$	−8.34024	+	25.6686i	−0.365393	+	1.12456i	0.584342	+	0.811507i	$0.301353\pi$
$521$	−8.34024	+	25.6686i	−0.365393	+	1.12456i	−0.949735	+	0.313056i	$0.898647\pi$
$522$	11.1389	−	1.33193i	0.487537	−	0.0582971i
$523$	25.2868	−	34.8043i	1.10571	−	1.52188i	0.278129	−	0.960544i	$-0.410286\pi$
$523$	25.2868	−	34.8043i	1.10571	−	1.52188i	0.827585	−	0.561341i	$-0.189714\pi$
$524$	6.65752	−	16.1824i	0.290835	−	0.706932i
$525$	−0.806375	−	2.48177i	−0.0351931	−	0.108313i
$526$	6.32010	−	31.9738i	0.275570	−	1.39412i
$527$	5.24004			0.228260
$528$	−10.5681	+	8.01968i	−0.459917	+	0.349012i
$529$	20.8992			0.908662
$530$	−2.09921	+	10.6200i	−0.0911839	+	0.461305i
$531$	3.69578	+	11.3745i	0.160383	+	0.493609i
$532$	0.445789	−	1.08358i	0.0193274	−	0.0469790i
$533$	6.69673	−	9.21726i	0.290067	−	0.399244i
$534$	−15.3354	+	1.83373i	−0.663629	+	0.0793533i
$535$	−3.92154	+	12.0692i	−0.169543	+	0.521799i
$536$	−15.5512	+	23.4563i	−0.671708	+	1.01316i
$537$	18.6164	−	13.5256i	0.803359	−	0.583674i
$538$	−9.26143	−	9.99487i	−0.399288	−	0.430909i
$539$	−7.85062	−	14.8158i	−0.338150	−	0.638162i
$540$	−3.52736	−	0.269093i	−0.151793	−	0.0115799i
$541$	−16.3673	+	11.8916i	−0.703686	+	0.511258i	−0.881131	−	0.472873i	$-0.843217\pi$
$541$	−16.3673	+	11.8916i	−0.703686	+	0.511258i	0.177444	+	0.984131i	$0.443217\pi$
$542$	−28.9817	−	16.1849i	−1.24487	−	0.695199i
$543$	−18.5589	−	6.03014i	−0.796437	−	0.258778i
$544$	−0.709967	+	21.3317i	−0.0304396	+	0.914588i
$545$	−9.75224	+	13.4228i	−0.417740	+	0.574970i
$546$	2.72574	+	5.89398i	0.116651	+	0.252239i
$547$	13.6380	−	4.43124i	0.583117	−	0.189466i	−0.00257925	−	0.999997i	$-0.500821\pi$
$547$	13.6380	−	4.43124i	0.583117	−	0.189466i	0.585697	+	0.810530i	$0.300821\pi$
$548$	−8.87806	−	14.4099i	−0.379252	−	0.615562i
$549$	−10.4503			−0.446010
$550$	−8.28595	−	2.89568i	−0.353314	−	0.123472i
$551$			3.33267i			0.141977i
$552$	1.09857	−	3.94960i	0.0467581	−	0.168106i
$553$	−2.50210	−	7.70067i	−0.106400	−	0.327466i
$554$	11.8362	+	25.5939i	0.502873	+	1.08738i
$555$	−13.4196	−	9.74989i	−0.569629	−	0.413860i
$556$	8.73842	+	7.42712i	0.370591	+	0.314980i
$557$	−9.72693	+	29.9364i	−0.412143	+	1.26845i	0.502638	+	0.864497i	$0.332363\pi$
$557$	−9.72693	+	29.9364i	−0.412143	+	1.26845i	−0.914781	+	0.403949i	$0.867637\pi$
$558$	0.957635	−	1.71480i	0.0405399	−	0.0725934i
$559$	−6.97434	−	9.59936i	−0.294983	−	0.406010i
$560$	1.49660	−	9.75185i	0.0632427	−	0.412091i
$561$	−8.98922	−	8.70559i	−0.379525	−	0.367550i
$562$	6.11206	+	6.59609i	0.257822	+	0.278239i
$563$	11.5320	+	15.8725i	0.486017	+	0.668946i	0.979647	−	0.200726i	$-0.0643302\pi$
$563$	11.5320	+	15.8725i	0.486017	+	0.668946i	−0.493630	+	0.869672i	$0.664330\pi$
$564$	0.360679	+	1.48661i	0.0151873	+	0.0625975i
$565$	3.08122	+	1.00115i	0.129628	+	0.0421187i
$566$	1.46537	+	12.2548i	0.0615940	+	0.515109i
$567$	−1.12813	−	0.819637i	−0.0473771	−	0.0344215i
$568$	−12.7365	−	34.1448i	−0.534412	−	1.43268i
$569$	25.2020	−	8.18862i	1.05652	−	0.343285i	0.271297	−	0.962496i	$-0.412547\pi$
$569$	25.2020	−	8.18862i	1.05652	−	0.343285i	0.785225	+	0.619211i	$0.212547\pi$
$570$	0.203790	−	1.03099i	0.00853584	−	0.0431833i
$571$		−	15.2004i		−	0.636116i	−0.948071	−	0.318058i	$-0.896969\pi$
$571$		−	15.2004i		−	0.636116i	0.948071	−	0.318058i	$-0.103031\pi$
$572$	21.3294	+	4.70682i	0.891827	+	0.196802i
$573$		−	25.6011i		−	1.06950i
$574$	−6.69363	−	1.32310i	−0.279387	−	0.0552250i
$575$	2.57957	−	0.838154i	0.107576	−	0.0349534i
$576$	6.85104	+	4.13077i	0.285460	+	0.172115i
$577$	17.6624	+	12.8325i	0.735296	+	0.534224i	0.891234	−	0.453543i	$-0.149840\pi$
$577$	17.6624	+	12.8325i	0.735296	+	0.534224i	−0.155939	+	0.987767i	$0.549840\pi$
$578$	3.88158	−	0.464139i	0.161453	−	0.0193057i
$579$	−21.0211	−	6.83016i	−0.873606	−	0.283852i
$580$	6.61643	+	27.2709i	0.274732	+	1.13236i
$581$	12.3650	+	17.0190i	0.512987	+	0.706066i
$582$	14.3793	−	13.3241i	0.596040	−	0.552301i
$583$	2.47226	+	14.1387i	0.102390	+	0.585567i
$584$	21.3006	−	16.9167i	0.881425	−	0.700019i
$585$	3.42354	+	4.71210i	0.141546	+	0.194821i
$586$	−25.4708	−	14.2242i	−1.05219	−	0.587597i
$587$	7.06883	−	21.7556i	0.291762	−	0.897951i	−0.692528	−	0.721391i	$-0.743503\pi$
$587$	7.06883	−	21.7556i	0.291762	−	0.897951i	0.984290	−	0.176560i	$-0.0564969\pi$
$588$	−6.54811	+	7.70422i	−0.270040	+	0.317717i
$589$	0.472045	+	0.342961i	0.0194503	+	0.0141315i
$590$	−27.1539	+	12.5577i	−1.11791	+	0.516990i
$591$	5.63114	+	17.3309i	0.231634	+	0.712896i
$592$	17.1900	+	33.3407i	0.706504	+	1.37029i
$593$			13.3772i			0.549336i	0.961539	+	0.274668i	$0.0885679\pi$
$593$			13.3772i			0.549336i	−0.961539	+	0.274668i	$0.911432\pi$
$594$	−4.49171	+	1.35075i	−0.184297	+	0.0554218i
$595$	9.30620			0.381517
$596$	20.3304	+	32.9982i	0.832766	+	1.35166i
$597$	−12.6151	+	4.09891i	−0.516303	+	0.167757i
$598$	−6.12626	+	2.83316i	−0.250521	+	0.115857i
$599$	−13.8109	+	19.0091i	−0.564300	+	0.776692i	−0.991865	−	0.127292i	$-0.959371\pi$
$599$	−13.8109	+	19.0091i	−0.564300	+	0.776692i	0.427565	+	0.903984i	$0.359371\pi$
$600$	0.226838	+	5.28808i	0.00926063	+	0.215885i
$601$	11.5910	+	3.76616i	0.472809	+	0.153625i	0.535722	−	0.844394i	$-0.320039\pi$
$601$	11.5910	+	3.76616i	0.472809	+	0.153625i	−0.0629138	+	0.998019i	$0.520039\pi$
$602$	−3.46470	+	6.20412i	−0.141211	+	0.252861i
$603$	−8.04981	+	5.84853i	−0.327814	+	0.238171i
$604$	1.58630	−	20.7937i	0.0645454	−	0.846083i
$605$	19.4468	−	0.623576i	0.790626	−	0.0253520i
$606$	8.32680	−	7.71577i	0.338253	−	0.313432i
$607$	33.2882	−	24.1853i	1.35113	−	0.981652i	0.352173	−	0.935935i	$-0.385443\pi$
$607$	33.2882	−	24.1853i	1.35113	−	0.981652i	0.998954	−	0.0457169i	$-0.0145572\pi$
$608$	−1.46012	+	1.87518i	−0.0592155	+	0.0760486i
$609$	−3.41819	+	10.5201i	−0.138512	+	0.426296i
$610$	−3.10371	−	25.9563i	−0.125666	−	1.05094i
$611$	1.48041	−	2.03761i	0.0598911	−	0.0824330i
$612$	−2.87101	+	6.97856i	−0.116054	+	0.282092i
$613$	3.01493	+	9.27900i	0.121772	+	0.374775i	0.993299	−	0.115572i	$-0.0368701\pi$
$613$	3.01493	+	9.27900i	0.121772	+	0.374775i	−0.871527	+	0.490347i	$0.836870\pi$
$614$	34.2090	+	6.76192i	1.38056	+	0.272889i
$615$	−6.11992			−0.246779
$616$	−2.80330	−	12.7772i	−0.112948	−	0.514808i
$617$	−19.8476			−0.799035			−0.399518	−	0.916725i	$-0.630822\pi$
$617$	−19.8476			−0.799035			−0.399518	+	0.916725i	$0.630822\pi$
$618$	−17.1169	−	3.38341i	−0.688542	−	0.136101i
$619$	0.849909	+	2.61575i	0.0341607	+	0.105136i	0.966683	−	0.255977i	$-0.0823970\pi$
$619$	0.849909	+	2.61575i	0.0341607	+	0.105136i	−0.932522	+	0.361113i	$0.882397\pi$
$620$	4.54359	+	1.86926i	0.182475	+	0.0750711i
$621$	0.851938	−	1.17259i	0.0341871	−	0.0470545i
$622$	−4.29905	−	35.9528i	−0.172376	−	1.44158i
$623$	4.70597	−	14.4835i	0.188541	−	0.580269i
$624$	−2.12291	−	12.9994i	−0.0849843	−	0.520391i
$625$	9.82260	−	7.13654i	0.392904	−	0.285462i
$626$	4.04837	−	3.75129i	0.161805	−	0.149932i
$627$	−0.240006	−	1.37258i	−0.00958490	−	0.0548156i
$628$	35.4880	+	2.70729i	1.41613	+	0.108033i
$629$	−28.6253	+	20.7975i	−1.14136	+	0.829250i
$630$	1.70074	−	3.04545i	0.0677590	−	0.121334i
$631$	5.16849	+	1.67934i	0.205754	+	0.0668536i	0.410081	−	0.912049i	$-0.365500\pi$
$631$	5.16849	+	1.67934i	0.205754	+	0.0668536i	−0.204327	+	0.978903i	$0.565500\pi$
$632$	0.703855	+	16.4084i	0.0279979	+	0.652690i
$633$	11.2460	−	15.4787i	0.446987	−	0.615225i
$634$	8.18828	−	3.78677i	0.325198	−	0.150392i
$635$	−12.0186	+	3.90508i	−0.476943	+	0.154968i
$636$	7.36901	−	4.54010i	0.292200	−	0.180027i
$637$	16.6472			0.659588
$638$	21.2008	+	30.5756i	0.839349	+	1.21050i
$639$		−	12.8845i		−	0.509703i
$640$	−8.22515	+	18.2432i	−0.325128	+	0.721127i
$641$	−5.69933	−	17.5407i	−0.225110	−	0.692817i	−0.998280	−	0.0586191i	$-0.981330\pi$
$641$	−5.69933	−	17.5407i	−0.225110	−	0.692817i	0.773170	−	0.634198i	$-0.218670\pi$
$642$	9.20923	−	4.25892i	0.363459	−	0.168086i
$643$	−36.3473	−	26.4078i	−1.43340	−	1.04142i	−0.989372	−	0.145408i	$-0.953551\pi$
$643$	−36.3473	−	26.4078i	−1.43340	−	1.04142i	−0.444024	−	0.896015i	$-0.646449\pi$
$644$	3.08003	+	2.61784i	0.121370	+	0.103157i
$645$	−1.96956	+	6.06168i	−0.0775513	+	0.238678i
$646$	−1.95723	−	1.09302i	−0.0770062	−	0.0430042i
$647$	−12.0677	−	16.6098i	−0.474430	−	0.652997i	0.502993	−	0.864291i	$-0.332232\pi$
$647$	−12.0677	−	16.6098i	−0.474430	−	0.652997i	−0.977423	+	0.211294i	$0.932232\pi$
$648$	1.75905	+	2.21489i	0.0691019	+	0.0870092i
$649$	−27.5951	+	28.4942i	−1.08320	+	1.11849i
$650$	6.39218	−	5.92311i	0.250722	−	0.232324i
$651$	1.13832	+	1.56677i	0.0446144	+	0.0614065i
$652$	11.6343	−	2.82269i	0.455633	−	0.110545i
$653$	−4.82108	−	1.56646i	−0.188664	−	0.0613005i	0.213161	−	0.977017i	$-0.431624\pi$
$653$	−4.82108	−	1.56646i	−0.188664	−	0.0613005i	−0.401825	+	0.915717i	$0.631624\pi$
$654$	13.1716	−	1.57499i	0.515050	−	0.0615870i
$655$	12.5200	+	9.09632i	0.489197	+	0.355423i
$656$	12.3613	+	6.22383i	0.482627	+	0.243000i
$657$	9.14630	−	2.97181i	0.356831	−	0.115941i
$658$	−1.47973	−	0.292491i	−0.0576858	−	0.0114025i
$659$		−	24.6770i		−	0.961279i	−0.876918	−	0.480640i	$-0.840405\pi$
$659$		−	24.6770i		−	0.961279i	0.876918	−	0.480640i	$-0.159595\pi$
$660$	−4.68896	−	10.7552i	−0.182518	−	0.418646i
$661$		−	29.9755i		−	1.16591i	−0.812504	−	0.582956i	$-0.801896\pi$
$661$		−	29.9755i		−	1.16591i	0.812504	−	0.582956i	$-0.198104\pi$
$662$	−1.19230	+	6.03191i	−0.0463400	+	0.234437i
$663$	11.8161	−	3.83928i	0.458899	−	0.149105i
$664$	−14.9127	−	39.9788i	−0.578724	−	1.55148i
$665$	0.838342	+	0.609091i	0.0325095	+	0.0236196i
$666$	1.57461	+	13.1684i	0.0610150	+	0.510266i
$667$	−10.9347	−	3.55289i	−0.423393	−	0.137569i
$668$	10.1047	−	2.45158i	0.390961	−	0.0948545i
$669$	−1.01832	−	1.40160i	−0.0393707	−	0.0541891i
$670$	−16.9172	−	18.2569i	−0.653567	−	0.705325i
$671$	−16.2282	−	30.6260i	−0.626482	−	1.18230i
$672$	−6.53238	+	4.42172i	−0.251992	+	0.170572i
$673$	−0.00676354	−	0.00930921i	−0.000260715	−	0.000358844i	0.808887	−	0.587965i	$-0.200071\pi$
$673$	−0.00676354	−	0.00930921i	−0.000260715	−	0.000358844i	−0.809147	+	0.587606i	$0.800071\pi$
$674$	7.04557	−	12.6163i	0.271385	−	0.485960i
$675$	−0.578275	+	1.77975i	−0.0222578	+	0.0685025i
$676$	2.79367	−	3.28691i	0.107449	−	0.126420i
$677$	−0.292248	−	0.212331i	−0.0112320	−	0.00816054i	0.582155	−	0.813078i	$-0.302210\pi$
$677$	−0.292248	−	0.212331i	−0.0112320	−	0.00816054i	−0.593387	+	0.804917i	$0.702210\pi$
$678$	−1.08728	−	2.35107i	−0.0417568	−	0.0902924i
$679$	5.97313	+	18.3834i	0.229228	+	0.705491i
$680$	−18.1858	−	5.05833i	−0.697395	−	0.193978i
$681$		−	6.29873i		−	0.241368i
$682$	6.51254	+	0.143576i	0.249378	+	0.00549783i
$683$	16.8584			0.645070			0.322535	−	0.946557i	$-0.395465\pi$
$683$	16.8584			0.645070			0.322535	+	0.946557i	$0.395465\pi$
$684$	−0.715380	+	0.440751i	−0.0273533	+	0.0168525i
$685$	14.2362	−	4.62561i	0.543935	−	0.176735i
$686$	−9.97914	−	21.5783i	−0.381005	−	0.823863i
$687$	2.03611	−	2.80246i	0.0776824	−	0.106921i
$688$	10.1428	−	10.2406i	0.386690	−	0.390420i
$689$	−13.5531	−	4.40366i	−0.516331	−	0.167766i
$690$	3.16547	+	1.76776i	0.120507	+	0.0672976i
$691$	33.4931	−	24.3341i	1.27414	−	0.925714i	0.274777	−	0.961508i	$-0.411396\pi$
$691$	33.4931	−	24.3341i	1.27414	−	0.925714i	0.999359	+	0.0357938i	$0.0113959\pi$
$692$	−2.13610	+	28.0007i	−0.0812022	+	1.06443i
$693$	0.650187	−	4.57893i	0.0246986	−	0.173939i
$694$	−7.14886	−	7.71500i	−0.271367	−	0.292857i
$695$	−8.20552	+	5.96166i	−0.311253	+	0.226139i
$696$	12.3978	−	18.7000i	0.469939	−	0.708823i
$697$	−4.03403	+	12.4155i	−0.152800	+	0.470269i
$698$	−8.24617	+	0.986034i	−0.312122	+	0.0373219i
$699$	−8.63879	+	11.8903i	−0.326749	+	0.449732i
$700$	−4.82648	−	1.98564i	−0.182424	−	0.0750500i
$701$	−9.88537	−	30.4240i	−0.373365	−	1.14910i	−0.944575	−	0.328296i	$-0.893526\pi$
$701$	−9.88537	−	30.4240i	−0.373365	−	1.14910i	0.571210	−	0.820804i	$-0.306474\pi$
$702$	0.903025	−	4.56846i	0.0340825	−	0.172425i
$703$	−3.93989			−0.148596
$704$	−1.46686	+	26.4924i	−0.0552844	+	0.998471i
$705$	−1.35290			−0.0509532
$706$	−7.22950	+	36.5744i	−0.272086	+	1.37650i
$707$	3.45895	+	10.6455i	0.130087	+	0.400367i
$708$	22.1208	+	9.10058i	0.831349	+	0.342021i
$709$	20.2031	−	27.8072i	0.758743	−	1.04432i	−0.238574	−	0.971124i	$-0.576680\pi$
$709$	20.2031	−	27.8072i	0.758743	−	1.04432i	0.997318	−	0.0731963i	$-0.0233200\pi$
$710$	32.0022	−	3.82665i	1.20102	−	0.143612i
$711$	−1.79433	+	5.52238i	−0.0672926	+	0.207105i
$712$	−17.0686	+	25.7452i	−0.639674	+	0.964841i
$713$	−1.62851	+	1.18318i	−0.0609883	+	0.0443106i
$714$	−5.05724	−	5.45774i	−0.189262	−	0.204251i
$715$	−8.49302	+	17.3504i	−0.317621	+	0.648870i
$716$	3.50075	−	45.8890i	0.130829	−	1.71495i
$717$	16.3738	−	11.8962i	0.611489	−	0.444273i
$718$	−4.92502	−	2.75039i	−0.183800	−	0.102644i
$719$	−25.4856	−	8.28077i	−0.950452	−	0.308821i	−0.207553	−	0.978224i	$-0.566550\pi$
$719$	−25.4856	−	8.28077i	−0.950452	−	0.308821i	−0.742899	+	0.669403i	$0.766550\pi$
$720$	−4.97886	+	5.02688i	−0.185551	+	0.187341i
$721$	10.1124	−	13.9185i	0.376605	−	0.518353i
$722$	11.1739	+	24.1618i	0.415850	+	0.899208i
$723$	−8.33413	+	2.70792i	−0.309950	+	0.100709i
$724$	−33.2277	+	20.4718i	−1.23490	+	0.760830i
$725$	14.8444			0.551307
$726$	−10.9336	−	11.0660i	−0.405785	−	0.410697i
$727$		−	26.4551i		−	0.981165i	−0.871395	−	0.490583i	$-0.836784\pi$
$727$		−	26.4551i		−	0.981165i	0.871395	−	0.490583i	$-0.163216\pi$
$728$	12.5125	+	3.48031i	0.463744	+	0.128989i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	10.0977	+	21.8347i	0.373733	+	0.808138i
$731$	10.9990	+	7.99128i	0.406814	+	0.295568i
$732$	−13.5357	+	15.9255i	−0.500295	+	0.588625i
$733$	−0.587267	+	1.80742i	−0.0216912	+	0.0667586i	−0.961316	−	0.275447i	$-0.911174\pi$
$733$	−0.587267	+	1.80742i	−0.0216912	+	0.0667586i	0.939625	+	0.342206i	$0.111174\pi$
$734$	−22.8886	+	40.9858i	−0.844833	+	1.51281i
$735$	−5.25609	−	7.23439i	−0.193874	−	0.266845i
$736$	−4.59598	−	6.78982i	−0.169410	−	0.250276i
$737$	−29.6403	−	14.5089i	−1.09181	−	0.534441i
$738$	3.32573	+	3.58911i	0.122422	+	0.132117i
$739$	8.35357	+	11.4977i	0.307291	+	0.422950i	0.934534	−	0.355874i	$-0.115817\pi$
$739$	8.35357	+	11.4977i	0.307291	+	0.422950i	−0.627243	+	0.778824i	$0.715817\pi$
$740$	−32.2397	+	7.82195i	−1.18516	+	0.287541i
$741$	1.31573	+	0.427505i	0.0483344	+	0.0157048i
$742$	1.01328	+	8.47401i	0.0371986	+	0.311091i
$743$	−19.8113	−	14.3937i	−0.726806	−	0.528055i	0.161746	−	0.986832i	$-0.448288\pi$
$743$	−19.8113	−	14.3937i	−0.726806	−	0.528055i	−0.888551	+	0.458777i	$0.848288\pi$
$744$	−1.37286	−	3.68045i	−0.0503316	−	0.134932i
$745$	−32.6002	+	10.5924i	−1.19438	+	0.388077i
$746$	−8.42551	+	42.6252i	−0.308480	+	1.56062i
$747$		−	15.0860i		−	0.551966i
$748$	−24.9099	+	2.42304i	−0.910795	+	0.0885951i
$749$			10.0045i			0.365558i
$750$	−16.8621	−	3.33306i	−0.615719	−	0.121706i
$751$	38.6132	−	12.5462i	1.40901	−	0.457817i	0.496920	−	0.867796i	$-0.334464\pi$
$751$	38.6132	−	12.5462i	1.40901	−	0.457817i	0.912095	+	0.409980i	$0.134464\pi$
$752$	2.73265	+	1.37587i	0.0996493	+	0.0501729i
$753$	4.24381	+	3.08331i	0.154653	+	0.112362i
$754$	−36.6792	+	4.38591i	−1.33578	+	0.159725i
$755$	17.5407	+	5.69932i	0.638372	+	0.207420i
$756$	−2.71027	+	0.657562i	−0.0985716	+	0.0239153i
$757$	7.32712	+	10.0849i	0.266309	+	0.366542i	0.921139	−	0.389233i	$-0.127260\pi$
$757$	7.32712	+	10.0849i	0.266309	+	0.366542i	−0.654831	+	0.755776i	$0.727260\pi$
$758$	−38.0820	+	35.2875i	−1.38320	+	1.28170i
$759$	4.75939	+	0.675810i	0.172755	+	0.0245304i
$760$	−1.30719	−	1.64594i	−0.0474167	−	0.0597045i
$761$	19.4146	+	26.7219i	0.703779	+	0.968668i	0.999909	+	0.0135207i	$0.00430390\pi$
$761$	19.4146	+	26.7219i	0.703779	+	0.968668i	−0.296130	+	0.955148i	$0.595696\pi$
$762$	8.82141	+	4.92633i	0.319566	+	0.178462i
$763$	−4.04195	+	12.4399i	−0.146329	+	0.450353i
$764$	−39.0141	−	33.1596i	−1.41148	−	1.19967i
$765$	−5.39917	−	3.92273i	−0.195207	−	0.141827i
$766$	−16.0249	+	7.41091i	−0.579004	+	0.267767i
$767$	−12.1698	−	37.4548i	−0.439427	−	1.35242i
$768$	15.1687	−	5.09012i	0.547355	−	0.183674i
$769$		−	45.9291i		−	1.65625i	−0.560546	−	0.828123i	$-0.689409\pi$
$769$		−	45.9291i		−	1.65625i	0.560546	−	0.828123i	$-0.310591\pi$
$770$	11.5661	+	0.254989i	0.416814	+	0.00918915i
$771$	4.69434			0.169063
$772$	−37.6361	+	23.1878i	−1.35455	+	0.834548i
$773$	−13.4151	+	4.35884i	−0.482509	+	0.156777i	−0.540164	−	0.841560i	$-0.681638\pi$
$773$	−13.4151	+	4.35884i	−0.482509	+	0.156777i	0.0576547	+	0.998337i	$0.481638\pi$
$774$	4.62526	−	2.13901i	0.166251	−	0.0768850i
$775$	1.52762	−	2.10259i	0.0548737	−	0.0755272i
$776$	−1.68028	−	39.1708i	−0.0603184	−	1.40615i
$777$	−12.4369	−	4.04098i	−0.446170	−	0.144969i
$778$	22.9784	−	41.1467i	0.823816	−	1.47518i
$779$	−1.17600	+	0.854411i	−0.0421344	+	0.0306125i
$780$	11.6152	+	0.886092i	0.415891	+	0.0317272i
$781$	37.7596	−	20.0081i	1.35115	−	0.715947i
$782$	5.67282	−	5.25654i	0.202860	−	0.187973i
$783$	6.41754	−	4.66261i	0.229344	−	0.166628i
$784$	3.25926	+	19.9577i	0.116402	+	0.712774i
$785$	−9.72688	+	29.9363i	−0.347167	+	1.06847i
$786$	−1.46906	−	12.2857i	−0.0523996	−	0.438216i
$787$	−18.5090	+	25.4755i	−0.659776	+	0.908104i	−0.999474	−	0.0324309i	$-0.989675\pi$
$787$	−18.5090	+	25.4755i	−0.659776	+	0.908104i	0.339698	+	0.940535i	$0.389675\pi$
$788$	33.7046	+	13.8662i	1.20068	+	0.493964i
$789$	−7.12170	−	21.9184i	−0.253539	−	0.780314i
$790$	−14.2492	−	2.81658i	−0.506965	−	0.100209i
$791$	2.55411			0.0908138
$792$	−3.75942	+	8.59458i	−0.133585	+	0.305395i
$793$	34.4118			1.22200
$794$	−19.5649	−	3.86730i	−0.694333	−	0.137245i
$795$	2.36546	+	7.28014i	0.0838943	+	0.258200i
$796$	−10.0932	+	24.5336i	−0.357745	+	0.869570i
$797$	−19.3111	+	26.5794i	−0.684033	+	0.941490i	−0.999973	−	0.00728889i	$-0.997680\pi$
$797$	−19.3111	+	26.5794i	−0.684033	+	0.941490i	0.315941	+	0.948779i	$0.397680\pi$
$798$	−0.0983685	−	0.822653i	−0.00348221	−	0.0291216i
$799$	−0.891783	+	2.74463i	−0.0315490	+	0.0970979i
$800$	8.35245	+	6.50366i	0.295304	+	0.229939i
$801$	−8.83531	+	6.41923i	−0.312180	+	0.226812i
$802$	12.4054	−	11.4951i	0.438050	−	0.405906i
$803$	22.9124	+	22.1895i	0.808561	+	0.783050i
$804$	−1.51374	+	19.8426i	−0.0533854	+	0.699794i
$805$	−2.89220	+	2.10131i	−0.101937	+	0.0740614i
$806$	−3.15339	+	5.64666i	−0.111073	+	0.198895i
$807$	−9.16355	−	2.97742i	−0.322572	−	0.104810i
$808$	−0.973022	−	22.6832i	−0.0342308	−	0.797993i
$809$	3.52470	−	4.85134i	0.123922	−	0.170564i	−0.742549	−	0.669792i	$-0.766383\pi$
$809$	3.52470	−	4.85134i	0.123922	−	0.170564i	0.866470	+	0.499228i	$0.166383\pi$
$810$	−2.27043	+	1.04999i	−0.0797748	+	0.0368928i
$811$	−39.0150	+	12.6767i	−1.37000	+	0.445140i	−0.899369	−	0.437189i	$-0.855974\pi$
$811$	−39.0150	+	12.6767i	−1.37000	+	0.445140i	−0.470632	+	0.882330i	$0.655974\pi$
$812$	11.6045	+	18.8351i	0.407237	+	0.660984i
$813$	−23.4722			−0.823205
$814$	−36.1465	+	25.0636i	−1.26694	+	0.878480i
$815$			10.5879i			0.370876i
$816$	6.91614	+	13.4141i	0.242113	+	0.469589i
$817$	0.467812	+	1.43978i	0.0163667	+	0.0503714i
$818$	−20.9598	+	9.69310i	−0.732842	+	0.338911i
$819$	3.71482	+	2.69897i	0.129806	+	0.0943098i
$820$	−7.92678	+	9.32630i	−0.276815	+	0.325689i
$821$	7.86487	−	24.2056i	0.274486	−	0.844781i	−0.714869	−	0.699258i	$-0.753514\pi$
$821$	7.86487	−	24.2056i	0.274486	−	0.844781i	0.989355	−	0.145523i	$-0.0464863\pi$
$822$	−10.4490	−	5.83529i	−0.364452	−	0.203529i
$823$	8.33462	+	11.4716i	0.290526	+	0.399875i	0.929185	−	0.369615i	$-0.120510\pi$
$823$	8.33462	+	11.4716i	0.290526	+	0.399875i	−0.638659	+	0.769490i	$0.720510\pi$
$824$	−27.3266	+	21.7025i	−0.951967	+	0.756043i
$825$	−6.11376	+	1.06903i	−0.212854	+	0.0372190i
$826$	−17.3000	+	16.0305i	−0.601945	+	0.557773i
$827$	16.3323	+	22.4795i	0.567931	+	0.781690i	0.992308	−	0.123796i	$-0.0395068\pi$
$827$	16.3323	+	22.4795i	0.567931	+	0.781690i	−0.424377	+	0.905486i	$0.639507\pi$
$828$	−0.683476	−	2.81708i	−0.0237524	−	0.0979003i
$829$	−47.9834	−	15.5908i	−1.66653	−	0.541490i	−0.684308	−	0.729193i	$-0.739896\pi$
$829$	−47.9834	−	15.5908i	−1.66653	−	0.541490i	−0.982226	+	0.187703i	$0.939896\pi$
$830$	37.4701	−	4.48047i	1.30061	−	0.155520i
$831$	16.1312	+	11.7200i	0.559584	+	0.406561i
$832$	−22.5597	−	13.6022i	−0.782118	−	0.471570i
$833$	−18.1410	+	5.89437i	−0.628549	+	0.204228i
$834$	7.95539	+	1.57250i	0.275473	+	0.0544514i
$835$			9.19584i			0.318235i
$836$	−2.40258	−	1.41208i	−0.0830949	−	0.0488377i
$837$		−	1.38882i		−	0.0480045i
$838$	1.47251	−	7.44953i	0.0508671	−	0.257340i
$839$	44.3548	−	14.4117i	1.53130	−	0.497548i	0.582337	−	0.812947i	$-0.302138\pi$
$839$	44.3548	−	14.4117i	1.53130	−	0.497548i	0.948959	+	0.315399i	$0.102138\pi$
$840$	−2.43817	−	6.53640i	−0.0841250	−	0.225527i
$841$	−27.4457	−	19.9405i	−0.946403	−	0.687602i
$842$	1.57184	+	13.1452i	0.0541691	+	0.453015i
$843$	6.04746	+	1.96494i	0.208286	+	0.0676761i
$844$	−9.02219	−	37.1867i	−0.310557	−	1.28002i
$845$	2.24245	+	3.08646i	0.0771425	+	0.106178i
$846$	0.735203	+	0.793425i	0.0252768	+	0.0272785i
$847$	14.4288	−	5.20510i	0.495779	−	0.178849i
$848$	2.62589	−	17.1104i	0.0901734	−	0.587572i
$849$	5.12972	+	7.06045i	0.176052	+	0.242314i
$850$	−4.86853	+	8.71791i	−0.166989	+	0.299022i
$851$	4.20023	−	12.9270i	0.143982	−	0.443132i
$852$	−19.6350	−	16.6886i	−0.672685	−	0.571741i
$853$	41.5877	+	30.2152i	1.42394	+	1.03455i	0.991106	+	0.133073i	$0.0424846\pi$
$853$	41.5877	+	30.2152i	1.42394	+	1.03455i	0.432829	+	0.901476i	$0.357515\pi$
$854$	−8.65044	−	18.7052i	−0.296012	−	0.640078i
$855$	−0.229638	−	0.706752i	−0.00785345	−	0.0241704i
$856$	5.43791	−	19.5505i	0.185864	−	0.668222i
$857$		−	17.4541i		−	0.596221i	−0.954531	−	0.298111i	$-0.903644\pi$
$857$		−	17.4541i		−	0.596221i	0.954531	−	0.298111i	$-0.0963565\pi$
$858$	14.7907	−	4.44786i	0.504947	−	0.151847i
$859$	−35.3164			−1.20498			−0.602489	−	0.798127i	$-0.705824\pi$
$859$	−35.3164			−1.20498			−0.602489	+	0.798127i	$0.705824\pi$
$860$	6.68649	+	10.8528i	0.228007	+	0.370077i
$861$	−4.58855	+	1.49091i	−0.156377	+	0.0508101i
$862$	22.7043	+	49.0944i	0.773312	+	1.67216i
$863$	3.84304	−	5.28949i	0.130819	−	0.180056i	−0.738583	−	0.674163i	$-0.764505\pi$
$863$	3.84304	−	5.28949i	0.130819	−	0.180056i	0.869401	+	0.494106i	$0.164505\pi$
$864$	5.65372	+	0.188169i	0.192344	+	0.00640164i
$865$	−23.6202	−	7.67468i	−0.803112	−	0.260947i
$866$	−12.2841	−	6.86010i	−0.417432	−	0.233116i
$867$	2.23632	−	1.62478i	0.0759495	−	0.0551805i
$868$	3.86204	+	0.294625i	0.131086	+	0.0100002i
$869$	−18.9704	+	3.31711i	−0.643526	+	0.112525i
$870$	13.4868	+	14.5549i	0.457247	+	0.493458i
$871$	26.5071	−	19.2586i	0.898160	−	0.652552i
$872$	14.6602	−	22.1125i	0.496459	−	0.748824i
$873$	4.28351	−	13.1833i	0.144975	−	0.446186i
$874$	0.855073	−	0.102245i	0.0289233	−	0.00345849i
$875$	9.96190	−	13.7114i	0.336774	−	0.463529i
$876$	7.31786	−	17.7875i	0.247247	−	0.600984i
$877$	−9.06904	−	27.9116i	−0.306240	−	0.942509i	−0.979212	−	0.202841i	$-0.934982\pi$
$877$	−9.06904	−	27.9116i	−0.306240	−	0.942509i	0.672972	−	0.739668i	$-0.265018\pi$
$878$	−4.35606	+	22.0376i	−0.147010	+	0.743732i
$879$	−20.6288			−0.695790
$880$	−22.4635	−	6.78499i	−0.757244	−	0.228722i
$881$	1.12915			0.0380420			0.0190210	−	0.999819i	$-0.493945\pi$
$881$	1.12915			0.0380420			0.0190210	+	0.999819i	$0.493945\pi$
$882$	−1.38640	+	7.01386i	−0.0466824	+	0.236169i
$883$	4.24530	+	13.0657i	0.142866	+	0.439695i	0.996730	−	0.0807999i	$-0.0257475\pi$
$883$	4.24530	+	13.0657i	0.142866	+	0.439695i	−0.853865	+	0.520495i	$0.825747\pi$
$884$	9.45393	−	22.9796i	0.317970	−	0.772889i
$885$	−12.4343	+	17.1144i	−0.417975	+	0.575294i
$886$	−7.61649	+	0.910740i	−0.255881	+	0.0305969i
$887$	−1.98190	+	6.09967i	−0.0665458	+	0.204807i	−0.978800	−	0.204817i	$-0.934340\pi$
$887$	−1.98190	+	6.09967i	−0.0665458	+	0.204807i	0.912254	+	0.409624i	$0.134340\pi$
$888$	22.1072	+	14.6567i	0.741869	+	0.491847i
$889$	−8.05988	+	5.85584i	−0.270320	+	0.196399i
$890$	−18.5679	−	20.0384i	−0.622399	−	0.671688i
$891$	−2.30732	+	2.38249i	−0.0772982	+	0.0798165i
$892$	−3.45491	−	0.263566i	−0.115679	−	0.00882485i
$893$	−0.259972	+	0.188880i	−0.00869962	+	0.00632064i
$894$	23.9279	+	13.3626i	0.800268	+	0.446911i
$895$	38.7101	+	12.5777i	1.29394	+	0.420426i
$896$	−1.72265	+	15.6821i	−0.0575498	+	0.523901i
$897$	−2.80534	+	3.86122i	−0.0936675	+	0.128922i
$898$	5.90839	+	12.7759i	0.197166	+	0.426339i
$899$	−10.4776	+	3.40438i	−0.349447	+	0.113542i
$900$	1.96320	+	3.18645i	0.0654399	+	0.106215i
$901$	16.3284			0.543979
$902$	−5.35384	+	15.3199i	−0.178263	+	0.510098i
$903$			5.02470i			0.167211i
$904$	−4.99115	−	1.38827i	−0.166003	−	0.0461733i
$905$	−10.6661	−	32.8270i	−0.354554	−	1.09121i
$906$	−6.18966	−	13.3841i	−0.205638	−	0.444658i
$907$	9.91808	+	7.20591i	0.329325	+	0.239268i	0.740144	−	0.672448i	$-0.234757\pi$
$907$	9.91808	+	7.20591i	0.329325	+	0.239268i	−0.410819	+	0.911717i	$0.634757\pi$
$908$	−9.59880	−	8.15839i	−0.318547	−	0.270746i
$909$	2.48051	−	7.63423i	0.0822733	−	0.253211i
$910$	−5.60035	+	10.0283i	−0.185650	+	0.332436i
$911$	21.4231	+	29.4864i	0.709779	+	0.976927i	0.999802	+	0.0199074i	$0.00633714\pi$
$911$	21.4231	+	29.4864i	0.709779	+	0.976927i	−0.290023	+	0.957020i	$0.593663\pi$
$912$	−0.254920	+	1.66106i	−0.00844125	+	0.0550034i
$913$	44.2113	−	23.4267i	1.46318	−	0.775312i
$914$	24.1196	+	26.0297i	0.797806	+	0.860986i
$915$	−10.8650	−	14.9544i	−0.359185	−	0.494376i
$916$	−1.63349	−	6.73275i	−0.0539720	−	0.222456i
$917$	11.6032	+	3.77010i	0.383170	+	0.124500i
$918$	0.633522	+	5.29813i	0.0209094	+	0.174864i
$919$	10.4315	+	7.57891i	0.344103	+	0.250005i	0.746391	−	0.665508i	$-0.231785\pi$
$919$	10.4315	+	7.57891i	0.344103	+	0.250005i	−0.402288	+	0.915513i	$0.631785\pi$
$920$	6.79399	−	2.53426i	0.223991	−	0.0835521i
$921$	23.4506	−	7.61956i	0.772724	−	0.251073i
$922$	9.46313	−	47.8745i	0.311652	−	1.57666i
$923$			42.4273i			1.39651i
$924$	−6.13580	−	6.92167i	−0.201853	−	0.227706i
$925$			17.5491i			0.577010i
$926$	31.6153	+	6.24925i	1.03894	+	0.205363i
$927$	−11.7338	+	3.81254i	−0.385389	+	0.125220i
$928$	−12.4393	−	43.1145i	−0.408339	−	1.41530i
$929$	11.5280	+	8.37561i	0.378223	+	0.274795i	0.760612	−	0.649206i	$-0.224899\pi$
$929$	11.5280	+	8.37561i	0.378223	+	0.274795i	−0.382390	+	0.924001i	$0.624899\pi$
$930$	3.44950	−	0.412473i	0.113114	−	0.0135255i
$931$	−2.02001	−	0.656340i	−0.0662031	−	0.0215107i
$932$	6.93056	+	28.5657i	0.227018	+	0.935700i
$933$	−15.0494	−	20.7137i	−0.492695	−	0.678137i
$934$	6.34426	−	5.87870i	0.207590	−	0.192357i
$935$	3.11175	−	21.9145i	0.101765	−	0.716680i
$936$	−5.79235	−	7.29340i	−0.189329	−	0.238392i
$937$	−29.3763	−	40.4330i	−0.959681	−	1.32089i	−0.947090	−	0.320967i	$-0.895992\pi$
$937$	−29.3763	−	40.4330i	−0.959681	−	1.32089i	−0.0125913	−	0.999921i	$-0.504008\pi$
$938$	−17.1317	−	9.56723i	−0.559370	−	0.312381i
$939$	1.20599	−	3.71165i	0.0393559	−	0.121125i
$940$	−1.75233	+	2.06172i	−0.0571549	+	0.0672459i
$941$	3.47674	+	2.52600i	0.113338	+	0.0823452i	0.643011	−	0.765857i	$-0.277685\pi$
$941$	3.47674	+	2.52600i	0.113338	+	0.0823452i	−0.529672	+	0.848202i	$0.677685\pi$
$942$	22.8423	−	10.5637i	0.744244	−	0.344185i
$943$	−1.54967	−	4.76938i	−0.0504641	−	0.155312i
$944$	42.5203	−	21.9229i	1.38392	−	0.713530i
$945$		−	2.46651i		−	0.0802354i
$946$	13.4511	+	10.2333i	0.437333	+	0.332712i
$947$	0.231238			0.00751424			0.00375712	−	0.999993i	$-0.498804\pi$
$947$	0.231238			0.00751424			0.00375712	+	0.999993i	$0.498804\pi$
$948$	6.09159	+	9.88724i	0.197846	+	0.321123i
$949$	−30.1178	+	9.78586i	−0.977664	+	0.317662i
$950$	−1.00917	+	0.466701i	−0.0327417	+	0.0151418i
$951$	3.74958	−	5.16085i	0.121588	−	0.167352i
$952$	−14.8675	+	0.637759i	−0.481859	+	0.0206699i
$953$	50.8341	+	16.5170i	1.64668	+	0.535039i	0.978017	−	0.208527i	$-0.0668670\pi$
$953$	50.8341	+	16.5170i	1.64668	+	0.535039i	0.668663	+	0.743566i	$0.266867\pi$
$954$	2.98407	−	5.34348i	0.0966130	−	0.173001i
$955$	36.6349	−	26.6168i	1.18548	−	0.861301i
$956$	3.07903	−	40.3609i	0.0995828	−	1.30536i
$957$	23.6301	+	11.5669i	0.763851	+	0.373904i
$958$	−3.21755	+	2.98144i	−0.103954	+	0.0963259i
$959$	9.54701	−	6.93631i	0.308289	−	0.223985i
$960$	1.21177	+	14.0984i	0.0391096	+	0.455025i
$961$	8.98349	−	27.6483i	0.289790	−	0.891882i
$962$	−5.18503	−	43.3622i	−0.167172	−	1.39805i
$963$	4.21709	−	5.80433i	0.135894	−	0.187042i
$964$	−6.66805	+	16.2080i	−0.214763	+	0.522025i
$965$	−12.0812	−	37.1821i	−0.388908	−	1.19694i
$966$	2.80404	+	0.554261i	0.0902185	+	0.0178331i
$967$	−1.08508			−0.0348938			−0.0174469	−	0.999848i	$-0.505554\pi$
$967$	−1.08508			−0.0348938			−0.0174469	+	0.999848i	$0.505554\pi$
$968$	−31.0254	+	2.32892i	−0.997194	+	0.0748545i
$969$	−1.58516			−0.0509225
$970$	34.0164	+	6.72386i	1.09220	+	0.215890i
$971$	−10.1034	−	31.0950i	−0.324233	−	0.997887i	−0.971786	−	0.235866i	$-0.924207\pi$
$971$	−10.1034	−	31.0950i	−0.324233	−	0.997887i	0.647552	−	0.762021i	$-0.275793\pi$
$972$	1.84959	+	0.760930i	0.0593256	+	0.0244068i
$973$	−4.69992	+	6.46889i	−0.150673	+	0.207383i
$974$	3.55325	+	29.7158i	0.113854	+	0.952154i
$975$	1.90420	−	5.86052i	0.0609831	−	0.187687i
$976$	6.73727	+	41.2549i	0.215655	+	1.32054i
$977$	−40.9534	+	29.7544i	−1.31021	+	0.951926i	−0.310215	+	0.950667i	$0.600401\pi$
$977$	−40.9534	+	29.7544i	−1.31021	+	0.951926i	−0.999999	+	0.00125964i	$0.999599\pi$
$978$	6.20938	−	5.75373i	0.198554	−	0.183984i
$979$	−32.5325	−	15.9246i	−1.03974	−	0.508954i
$980$	−17.8326	−	1.36040i	−0.569641	−	0.0434564i
$981$	7.58864	−	5.51347i	0.242287	−	0.176032i
$982$	−3.60049	+	6.44728i	−0.114896	+	0.205741i
$983$	−23.1688	−	7.52801i	−0.738971	−	0.240106i	−0.0847421	−	0.996403i	$-0.527007\pi$
$983$	−23.1688	−	7.52801i	−0.738971	−	0.240106i	−0.654229	+	0.756297i	$0.727007\pi$
$984$	9.77715	−	0.419402i	0.311684	−	0.0133700i
$985$	−18.9457	+	26.0766i	−0.603662	+	0.830869i
$986$	38.4175	−	17.7667i	1.22346	−	0.565806i
$987$	−1.01437	+	0.329588i	−0.0322877	+	0.0104909i
$988$	2.35567	−	1.45134i	0.0749438	−	0.0461734i
$989$	−5.22272			−0.166073
$990$	−6.60283	−	5.02326i	−0.209852	−	0.159650i
$991$			27.0358i			0.858821i	0.903110	+	0.429410i	$0.141279\pi$
$991$			27.0358i			0.858821i	−0.903110	+	0.429410i	$0.858721\pi$
$992$	−7.38692	−	2.67494i	−0.234535	−	0.0849293i
$993$	1.34352	+	4.13494i	0.0426354	+	0.131218i
$994$	23.0621	−	10.6654i	0.731486	−	0.338285i
$995$	−18.9812	−	13.7906i	−0.601743	−	0.437192i
$996$	−22.9899	−	19.5400i	−0.728462	−	0.619148i
$997$	−4.82347	+	14.8451i	−0.152761	+	0.470149i	−0.997927	−	0.0643542i	$-0.979501\pi$
$997$	−4.82347	+	14.8451i	−0.152761	+	0.470149i	0.845166	+	0.534503i	$0.179501\pi$
$998$	39.3492	+	21.9746i	1.24558	+	0.695595i
$999$	5.51214	+	7.58682i	0.174397	+	0.240036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.2.z.b.19.7	yes	48
3.2	odd	2		792.2.bp.d.19.6		48
4.3	odd	2		1056.2.bp.a.943.9		48
8.3	odd	2	inner	264.2.z.b.19.1	✓	48
8.5	even	2		1056.2.bp.a.943.4		48
11.7	odd	10	inner	264.2.z.b.139.1	yes	48
24.11	even	2		792.2.bp.d.19.12		48
33.29	even	10		792.2.bp.d.667.12		48
44.7	even	10		1056.2.bp.a.271.4		48
88.29	odd	10		1056.2.bp.a.271.9		48
88.51	even	10	inner	264.2.z.b.139.7	yes	48
264.227	odd	10		792.2.bp.d.667.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.z.b.19.1	✓	48	8.3	odd	2	inner
264.2.z.b.19.7	yes	48	1.1	even	1	trivial
264.2.z.b.139.1	yes	48	11.7	odd	10	inner
264.2.z.b.139.7	yes	48	88.51	even	10	inner
792.2.bp.d.19.6		48	3.2	odd	2
792.2.bp.d.19.12		48	24.11	even	2
792.2.bp.d.667.6		48	264.227	odd	10
792.2.bp.d.667.12		48	33.29	even	10
1056.2.bp.a.271.4		48	44.7	even	10
1056.2.bp.a.271.9		48	88.29	odd	10
1056.2.bp.a.943.4		48	8.5	even	2
1056.2.bp.a.943.9		48	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.274235 - 1.38737i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-1.84959 - 0.760930i) q^{4} +(1.03968 - 1.43099i) q^{5} +(-1.40421 + 0.167908i) q^{6} +(0.430909 - 1.32620i) q^{7} +(-1.56291 + 2.35739i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-1.70020 - 1.83484i) q^{10} +(-2.97889 - 1.45816i) q^{11} +(-0.152133 + 1.99421i) q^{12} +(2.66400 - 1.93551i) q^{13} +(-1.72176 - 0.961520i) q^{14} +(-1.68223 - 0.546590i) q^{15} +(2.84197 + 2.81482i) q^{16} +(-2.21773 + 3.05245i) q^{17} +(0.593615 + 1.28360i) q^{18} +(-0.399566 + 0.129827i) q^{19} +(-3.01186 + 1.85563i) q^{20} -1.39445 q^{21} +(-2.83992 + 3.73294i) q^{22} -1.44940i q^{23} +(2.72498 + 0.757945i) q^{24} +(0.578275 + 1.77975i) q^{25} +(-1.95471 - 4.22674i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.80615 + 2.12504i) q^{28} +(2.45128 - 7.54427i) q^{29} +(-1.21965 + 2.18398i) q^{30} +(-0.816325 - 1.12358i) q^{31} +(4.68456 - 3.17094i) q^{32} +(-0.466268 + 3.28369i) q^{33} +(3.62669 + 3.91390i) q^{34} +(-1.44978 - 1.99544i) q^{35} +(1.94361 - 0.471557i) q^{36} +(8.91884 + 2.89791i) q^{37} +(0.0705429 + 0.589948i) q^{38} +(-2.66400 - 1.93551i) q^{39} +(1.74848 + 4.68744i) q^{40} +(3.29058 - 1.06918i) q^{41} +(-0.382407 + 1.93462i) q^{42} -3.60336i q^{43} +(4.40016 + 4.96373i) q^{44} +1.76880i q^{45} +(-2.01086 - 0.397477i) q^{46} +(0.727433 - 0.236357i) q^{47} +(1.79883 - 3.57270i) q^{48} +(4.08999 + 2.97155i) q^{49} +(2.62775 - 0.314213i) q^{50} +(3.58836 + 1.16593i) q^{51} +(-6.40011 + 1.55278i) q^{52} +(-2.54374 - 3.50116i) q^{53} +(1.03734 - 0.961215i) q^{54} +(-5.18369 + 2.74674i) q^{55} +(2.45290 + 3.08856i) q^{56} +(0.246945 + 0.339891i) q^{57} +(-9.79446 - 5.46973i) q^{58} +(3.69578 - 11.3745i) q^{59} +(2.69552 + 2.29103i) q^{60} +(8.45451 + 6.14256i) q^{61} +(-1.78268 + 0.824422i) q^{62} +(0.430909 + 1.32620i) q^{63} +(-3.11460 - 7.36880i) q^{64} -5.82447i q^{65} +(4.42782 + 1.54739i) q^{66} +9.95011 q^{67} +(6.42459 - 3.95824i) q^{68} +(-1.37846 + 0.447890i) q^{69} +(-3.16600 + 1.46415i) q^{70} +(-7.57332 + 10.4238i) q^{71} +(-0.121217 - 2.82583i) q^{72} +(-9.14630 - 2.97181i) q^{73} +(6.46632 - 11.5790i) q^{74} +(1.51394 - 1.09994i) q^{75} +(0.837822 + 0.0639152i) q^{76} +(-3.21744 + 3.32227i) q^{77} +(-3.41583 + 3.16518i) q^{78} +(4.69761 - 3.41302i) q^{79} +(6.98271 - 1.14034i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.580949 - 4.85846i) q^{82} +(-8.86730 + 12.2048i) q^{83} +(2.57916 + 1.06108i) q^{84} +(2.06230 + 6.34711i) q^{85} +(-4.99919 - 0.988166i) q^{86} -7.93251 q^{87} +(8.09320 - 4.74342i) q^{88} +10.9210 q^{89} +(2.45398 + 0.485067i) q^{90} +(-1.41893 - 4.36703i) q^{91} +(-1.10289 + 2.68080i) q^{92} +(-0.816325 + 1.12358i) q^{93} +(-0.128428 - 1.07404i) q^{94} +(-0.229638 + 0.706752i) q^{95} +(-4.46336 - 3.47541i) q^{96} +(-11.2144 + 8.14771i) q^{97} +(5.24426 - 4.85943i) q^{98} +(3.26706 - 0.571268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{3} + 4 q^{4} - 12 q^{9} + 4 q^{11} + 6 q^{12} - 16 q^{14} + 20 q^{16} - 5 q^{18} + 25 q^{20} + 3 q^{22} + 20 q^{24} - 4 q^{25} + 4 q^{26} + 12 q^{27} - 25 q^{28} - 10 q^{30} - 4 q^{33} + 4 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) \) 48 * q + 12 * q^3 + 4 * q^4 - 12 * q^9 + 4 * q^11 + 6 * q^12 - 16 * q^14 + 20 * q^16 - 5 * q^18 + 25 * q^20 + 3 * q^22 + 20 * q^24 - 4 * q^25 + 4 * q^26 + 12 * q^27 - 25 * q^28 - 10 * q^30 - 4 * q^33 + 4 * q^36 + 26 * q^38 - 65 * q^40 - 60 * q^41 - 4 * q^42 - 43 * q^44 - 5 * q^46 + 5 * q^48 - 12 * q^49 - 80 * q^50 - 15 * q^52 - 14 * q^56 + 73 * q^58 - 8 * q^59 - 25 * q^60 - 45 * q^62 - 38 * q^64 - 13 * q^66 + 8 * q^67 - 55 * q^68 - 40 * q^70 + 20 * q^72 + 60 * q^74 - 36 * q^75 + 46 * q^78 - 12 * q^81 - 35 * q^82 - 100 * q^83 + 45 * q^84 + 81 * q^86 - 18 * q^88 + 96 * q^89 + 10 * q^90 - 20 * q^91 + 59 * q^92 + 35 * q^94 - 40 * q^97 - 16 * q^99

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